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  • 1
    Electronic Resource
    Electronic Resource
    Stabilization of smoothness priors time-varying autoregressive models (2000)
    Springer
    Circuits, systems and signal processing 19 (2000), S. 423-435 
    Details
    ISSN: 1531-5878
    Keywords: Time-varying autoregressive models ; stability ; smoothness priors ; Tihkonov regularization ; constrained optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The stability of time-varying autoregressive (AR) models is an important issue in such applications as time-varying spectrum estimation and electroencephalography simulation and estimation. In some cases, such as time-varying spectrum estimation, the models that exhibit roots near unit moduli are difficult to use. Thus a tighter stability condition such as stability with a positive margin is needed. A time-varying AR model is stable with a positive margin if the moduli of the roots of the time-varying characteristic polynomial are somewhat less than unity for every time instant. Recently, a new method for the estimation of the time-varying AR models was introduced. This method is based on the interpretation of the underdetermined time-varying prediction equations as an ill-posed inverse problem that is solved by Tikhonov regularization. The method is referred to as the deterministic regression smoothness priors (DRSP) scheme. In this paper, a stabilization method in which the DRSP scheme is augmented with nonlinear stability constrainst is proposed. The problem is formulated so that stability with a positive margin can also be achieved. The problem is solved iteratively with an exterior point algorithm. The performance of the algorithm is studied with a simulation. It is shown that the proposed approach is well suited to stable modeling of signals containing narrowband transitions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01196156
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of constant coefficient linear singular systems with delay (2000)
    Springer
    Circuits, systems and signal processing 19 (2000), S. 13-25 
    Details
    ISSN: 1531-5878
    Keywords: Singular systems ; delay ; consistency condition ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, the general class of singular systems with delay and linear constant coefficient singular systems with delay are discussed. First, several definitions of stability are presented for singular systems with delay, and general sufficient stability conditions and instability conditions are obtained. Second, stability and instability are analyzed for linear constant coefficient singular systems with delay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229989
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  • 3
    Electronic Resource
    Electronic Resource
    A structural approach to robust stability of polynomials (1992)
    Springer
    Multidimensional systems and signal processing 3 (1992), S. 421-425 
    Details
    ISSN: 1573-0824
    Keywords: Convex combination ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A sufficient condition for Hurwitz stability of a convex combination of two stable polynomials is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01940234
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  • 4
    Electronic Resource
    Electronic Resource
    Stability regions of Schur andG-stable polynomials (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 91-101 
    Details
    ISSN: 1573-0824
    Keywords: Bilinear transformation ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The paper presents a unified approach to calculation, for a given, nominal,G-stable polynomial, a corresponding stability region in the space of perturbed coefficients
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00986008
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  • 5
    Electronic Resource
    Electronic Resource
    Stability determination of two-dimensional discrete-time systems (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 331-354 
    Details
    ISSN: 1573-0824
    Keywords: two-dimensional discrete-time systems ; two-dimensional digital filters ; bivariate polynomials ; stability ; Bistritz tabular form ; Jury tabular form ; Schur-Cohn minors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In determining root distribution of univariate polynomials with real or complex-valued coefficients, the Bistritz tabular form offers a significant computational advantage. Stability studies of two-dimensional (2-D) discrete-time systems involve univariate polynomials possessing parameter-dependent coefficients, where the parameter takes values on the unit circle in the complex plane. This paper investigates the application of Bistritz tabular form in determining stability of 2-D discrete-time systems, and for this purpose we present two algorithms. Both algorithms utilize a recent result that has established the relationship between Schur-Cohn minors and the entries of the Bistritz tabular form corresponding to a given polynomial. A comparison between the use of the modified Jury table and the Bistritz table in stability checking of 2-D discrete-time systems is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989650
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  • 6
    Electronic Resource
    Electronic Resource
    Acid-base equilibrium—A thermodynamic study of formation and stability of the Bi-2223 phase (1993)
    Springer
    Journal of superconductivity 6 (1993), S. 55-57 
    Details
    ISSN: 1572-9605
    Keywords: Superconductivity ; Bi-2223 ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A general acid-base equilibrium theory was proposed to explain the formation and stability of the Bi-2223 phase based on the Lewis acid-base theory, and principle of metallurgical physical chemistry. The acid-base nature of oxide was defined according to the electrostatic force between cation and oxygen anion. A series of experimental facts were systematically explained based on the theory: substitution of Bi for Ca in. the Pb-free 2223 phase, and the effect of substitution of the high-valent cation for Bi3+; oxygen-pressure atmosphere, and the heat-schocking technique on the formation and stability of the 2223 phase.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00618506
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  • 7
    Electronic Resource
    Electronic Resource
    Nondestructive evaluation of corrosion damage using electrostatic measurements (1995)
    Springer
    Journal of nondestructive evaluation 14 (1995), S. 127-136 
    Details
    ISSN: 1573-4862
    Keywords: Nondestructive evaluation ; corrosion monitoring ; electrical impedance tomography ; stability ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract We investigate the problem of detecting and assessing, by means of static electrical measurements, damage due to corrosion in a structure. Corrosion damage, which is assumed to occur in an inaccessible part of a specimen, is modelled as material loss. The detection device consists of electrodes which inject DC current and measure voltage potentials in the accessible part of the specimen. The topography of the damaged surface is estimated from the measured data. This research is meant to evaluate if a method based on static electrical measurements has the potential to be developed into a useful nondestructive evaluation tool. We propose computational methods that take the measured data and estimate the unknown damaged surface. The methods are studied in order to understand their properties. Several example calculations from synthetic data are presented. Our findings indicate that such a device has limited resolution. However, it offers several advantages that make it worthwhile to pursue further research.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183118
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  • 8
    Electronic Resource
    Electronic Resource
    Partial Compensation for Mismatched Uncertain Discrete Systems (2000)
    Springer
    Dynamics and control 10 (2000), S. 47-61 
    Details
    ISSN: 1573-8450
    Keywords: stability ; robust control ; Lyapunov approach ; discrete system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Control design of nonlinear discrete-time uncertain systems with (possibly fast) uncertain parameters is considered. We study the effect of only partially compensating the uncertainty. The optimal choice of a design parameter, which indicates the amount of compensation, is recommended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008395928788
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal Model Reduction with a Frequency Weighted Extension (2000)
    Springer
    Dynamics and control 10 (2000), S. 255-276 
    Details
    ISSN: 1573-8450
    Keywords: continuous-time systems ; frequency weighted model reduction ; gradient flow ; optimization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Inthis paper, a model reduction technique based on optimizationis presented. The objective function minimized is the impulseenergy of the overall system. An extension of the technique tothe frequency weighted case is also presented, where single-sidedor double-sided weightings can be incorporated in the reductionprocedure. The paper proposes an alternative to find an optimizationsolution by solving ordinary differential equations which aregradient flow associated with the objective function to be minimized.Two examples are presented to illustrate the effectiveness ofthe method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008366812002
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  • 10
    Electronic Resource
    Electronic Resource
    A Multistage Closed-loop Sigma-Delta modulator (MSCL) (1996)
    Springer
    Analog integrated circuits and signal processing 11 (1996), S. 195-204 
    Details
    ISSN: 1573-1979
    Keywords: A/D converters ; sigma-delta ; modulator ; band-pass ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new family of high order Sigma Delta modulators called MSCL (Multi Stage Closed-loop) is presented in this paper. They use a global feedback to lower the sensitivity to circuit imperfections. This feedback from the output of the modulator is the sum of the output of each comparator so that no digital prefiltering is required before summing up these signals. However, easy calibration will be required to compensate for the feedback imperfections. MSCL modulators present the same insensitivity to circuit imperfections as classical multi-order one-bit converters, but reach the performance of high-order MASH (MultistAge noise SHaping) modulators. They help make high-order low-pass or band-pass modulators without limit cycles so that their quantizing noise characteristics are similar to those predicted by the linear simplified model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00240484
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  • 11
    Electronic Resource
    Electronic Resource
    On the Global Dynamics of a Controlled Viscous Burgers' Equation (1998)
    Springer
    Journal of dynamical and control systems 4 (1998), S. 457-519 
    Details
    ISSN: 1573-8698
    Keywords: Boundary control ; nonlinear distributed parameter system ; center manifold theorem ; stability ; local attractors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we consider a boundary control problem for a forced Burgers' equation in a Hilbert state space consisting of square integrable functions on a finite interval. Our first main result consists in proving the global in time existence of solutions of the closed loop boundary control system for arbitrary L 2 initial data and quite general forcing terms (disturbances). For the unforced problem, our main interest is in stability of equilibria, while for the forced problem we are interested in steady state behavior of solutions. We note that the uncontrolled (open loop), unforced problem is not asymptotically stable on L 2. However, for positive gains we show that the unforced closed loop system is globally Lyapunov stable and locally exponentially stable. In addition, for nonzero stationary forcing, we show that there is a local absorbing ball and that the corresponding nonlinear semigroup is compact for all t 〉 0. Using this fact, we are able to deduce several consequences regarding the existence and properties of local attractors. Our method of proof is based on a systematic investigation of the smoothing properties of the controlled dynamics. In particular we establish various regularity results for the dynamics of the closed loop system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021815100868
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  • 12
    Electronic Resource
    Electronic Resource
    Control of Discrete Fuzzy Systems: Uncertainty and Guaranteed Performance (1998)
    Springer
    Dynamics and control 8 (1998), S. 83-106 
    Details
    ISSN: 1573-8450
    Keywords: fuzzy modeling ; robust control ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Robust control designs for a discrete Takagi and Sugeno (T-S) fuzzy model are proposed. The T-S fuzzy model contains (possibly fast) time-varying uncertainty. First, a switching-type robust control is shown to stabilize the T-S fuzzy model asymptotically. Second, a saturation-type robust control is shown to render the T-S model practically stable. In both designs, only the bound of uncertainty is needed. The effectiveness of proposed designs is analyzed rigorously and illustrated by simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008231013911
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  • 13
    Electronic Resource
    Electronic Resource
    A generalization of the Tikhonov theorem for singularly perturbed differential inclusions (1997)
    Springer
    Journal of dynamical and control systems 3 (1997), S. 291-319 
    Details
    ISSN: 1573-8698
    Keywords: 34D15 ; 34E15 ; 34A60 ; 93C73 ; 93D20 ; 49N99 ; Singular perturbation ; differential inclusion ; control systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study the continuity properties of the bundle of solutions to a differential inclusion subject to a singular perturbation, i.e., with respect to a scalar parameter ɛ multiplying a part of the derivatives. We give conditions under which every solution of the singularly perturbed inclusion is close, in a certain sense and for a sufficiently small ɛ, to a solution of the degenerate inclusion obtained for ɛ=0. These conditions include both stability and structural requirements (the later having no counterpart in the case of a differential equation). The main result obtained generalizes the well-known Tikhonov theorem for singularly perturbed differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463254
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  • 14
    Electronic Resource
    Electronic Resource
    On Invariant Manifolds in Singularly Perturbed Systems (1999)
    Springer
    Journal of dynamical and control systems 5 (1999), S. 501-507 
    Details
    ISSN: 1573-8698
    Keywords: Singular perturbation ; invariant manifold ; overflowing manifold ; stability ; characteristic numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A singularly perturbed system with a small parameter ε at the velocity of the slow variable y and with the fast variable x is considered. The main hypothesis is that for all y from some bounded domain D, the fast subsystem has a stable invariant or overflowing manifold M 0(y) and that the motions in this system going in the directions transversal to M 0(y) are more fast than the mutual approaching of trajectories on M 0(y) (a precise statement is given in terms of appropriate Lyapunov-type characteristic numbers). It is proved that for a sufficiently small ε, the whole system has an invariant manifold close to $$\bigcup\limits_{y \in D} {M_0 (y) \times \{ y\}}$$ the degree of its smoothness is specifed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021739205527
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  • 15
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    On the Stability of Nonconservative Systems with Estimation of the Attraction Domain (2000)
    Springer
    Journal of dynamical and control systems 6 (2000), S. 503-510 
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    ISSN: 1573-8698
    Keywords: nonconservative mechanical systems ; stability ; Lyapunov functions ; attraction domain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Mechanical systems subjected to dissipative, gyroscopic, conservative, and also nonconservative positional forces are considered. The question of the effect of dissipative, gyroscopic, and conservative forces on the motion stability of a mechanical systems is determined by classical Kelvin–Chetaev theorems [1]. The presence of nonconservative positional forces considerably complicates the situation and excludes direct application of these theorems. Applying Lyapunov's functions method the condition of asymptotic stability of a mechanical system under the action of all listed above forces is obtained. Moreover, the estimation of the attraction domain in phase space is found. The precession system which is used in the solution of some problems in the applied theory of the gyroscopic systems is also examined. The connection between the stability of origin and precession systems is detected. Theoretical results are applied to the stabilization problem of stationary motion of the balanced gimbal suspension gyro by means of external moments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009500527061
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  • 16
    Electronic Resource
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    Robust Stability of Multivariate Polynomials. Part 1: Small Coefficient Perturbations (1999)
    Springer
    Multidimensional systems and signal processing 10 (1999), S. 7-20 
    Details
    ISSN: 1573-0824
    Keywords: multivariate polynomials ; stability ; robust stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a detailed analysis of some classes of stable multivariate polynomials. The main aim of the analysis is to give conditions under which polynomials preserve stability when they are subjected to small coefficient variations. The maximal class of such polynomials is introduced. Some basic properties of polynomials from this class are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008456918178
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  • 17
    Electronic Resource
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    Numerical Investigation of a Stability Theorem Arising from the 2-Dimensional Analysis of an Iterative Optimal Control Algorithm (2000)
    Springer
    Multidimensional systems and signal processing 11 (2000), S. 109-124 
    Details
    ISSN: 1573-0824
    Keywords: 2-D linear systems ; optimal control ; stability ; unit memory linear repetitive processes ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Because many optimal control problems require solution using iterative procedures they fall naturally in the realm of 2-D systems where the two dimensions are response time horizon and iteration index, respectively. The paper uses this observation to employ 2-D systems theory, in the form of unit memory repetitive process techniques, to analyse local stability and convergence behaviour of a continuous optimal control algorithm based on dynamic system optimisation and parameter estimation. Existing work is extended to incorporate unmatched terminal constraints. Necessary and sufficient conditions for stability are obtained whose evaluation require the solution of a difficult eigenvalue problem. The paper shows how solutions can be achieved using numerical and graphical facilities of MATLAB.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008490731182
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  • 18
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    The Jump Behavior and Stability Analysis for 2-D Singular Systems (2000)
    Springer
    Multidimensional systems and signal processing 11 (2000), S. 339-358 
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    ISSN: 1573-0824
    Keywords: 2-D systems ; descriptor systems ; singular systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we discussthe jump behavior and stability problems for 2-D linear shift-invariantsingular systems under the standard boundary conditions. It isshown that once a boundary condition or the input is inadmissiblein the classical sense, a group of non-causal or backward jumpsof the system states will be incited. This interpretation releasesthe conventional admissibility constraints on the boundary conditionsand inputs. Based on this observation, a systematic stabilitytheory is developed for 2-D singular systems. The well-knownbasic stability theorem for the 1-D singular systems or 2-D regularsystems is thus extended to the 2-D singular case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008429611994
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  • 19
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    Stability tests and performance bounds for a class of 2D linear systems (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 355-391 
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    ISSN: 1573-0824
    Keywords: repetitive dynamics ; stability ; performance bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Repetitive, or multipass, processes are a class of 2D systems characterized by a recursive action with interaction between successive outputs or pass profiles. This interpass interaction is the source of the unique control problem for these processes in that it can cause the output sequence to exhibit oscillations which increase in amplitude from pass to pass. Previous work has developed an abstract stability theory and applied it to subclasses, such as discrete nonunit memory linear processes which are considered here, to produce basic stability tests. This article begins by reviewing the known stability tests and concludes that, at best, they only produce highly qualitative indicators of relative stability and performance. Hence, unlike (say) Bode and Nyquist tests for standard linear systems, they are of limited appeal as a basis for computer-aided control systems design. To remove this difficulty, step response data is used to develop new simulation-based tests which yield, at no extra cost, unique computable performance measures. Further, the undoubted advantages of having such measures available is clearly shown by developing a (virtually) complete solution to controller design for one subclass.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989651
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  • 20
    Electronic Resource
    Electronic Resource
    Eigenvalue localization ofG-stable matrix polytopes (1994)
    Springer
    Multidimensional systems and signal processing 5 (1994), S. 307-318 
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    ISSN: 1573-0824
    Keywords: Eigenvalue ; matrix ; polytope ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A simple geometric test can be applied to evaluateG-stability of a polytope of matrices. In case of a regionG being a convex subset of the complex plane, it suffices to assume that four (for some regions even less) corner points of a certain rectangle are contained inG.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00980713
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  • 21
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    An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems (1995)
    Springer
    Multidimensional systems and signal processing 6 (1995), S. 287-312 
    Details
    ISSN: 1573-0824
    Keywords: Two-dimensional discrete-time systems ; two-dimensional digital filters ; δ-operator formulated discrete-time systems ; bivariate polynomials ; Schur-Cohn minors ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The recent interest in delta-operator (or, δ-operator) formulated discrete-time systems (or, δ-systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or,q-operator) counterparts (or,q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the δ-operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementabledirect algorithm for stability checking of 2-D δ-system transfer function models.Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of δ-system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00983557
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  • 22
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    Destabilization via Active Stiffness (1997)
    Springer
    Dynamics and control 7 (1997), S. 263-268 
    Details
    ISSN: 1573-8450
    Keywords: Structural control ; active control ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In a recent paper leit one of the authors noted, without presenting aproof, that appropriate variation of the stiffness coefficient in amass-spring-damper system leads to increase of the system energy during acycle of the motion. Some have expressed doubt concerning the validity ofthis claim which implies that a damped simple oscillator can be destabilizedby varying the spring constant. It is the purpose of this note to present aproof.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008246401742
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