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  • 1
    Electronic Resource
    Electronic Resource
    Least squares completions for nonlinear differential algebraic equations (1993)
    Springer
    Numerische Mathematik 65 (1993), S. 77-94 
    Details
    ISSN: 0945-3245
    Keywords: 34A09 ; 65L05 ; 65H10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method has been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit Runge-Kutta may not be appropriate. This method is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. The theoretical foundations, generality, and limitations of this approach remain to be determined. This paper carefully examines several key aspects of this approach. The emphasis is on general results rather than specific results based on the structure of various applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385741
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  • 2
    Electronic Resource
    Electronic Resource
    The index of general nonlinear DAEs (1995)
    Springer
    Numerische Mathematik 72 (1995), S. 173-196 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65L20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In the last few years there has been considerable research on differential algebraic equations (DAEs) $F(t, y, y') = 0$ where $F_{y'}$ is identically singular. Much of the mathematical effort has focused on computing a solution that is assumed to exist. More recently there has been some discussion of solvability of DAEs. There has historically been some imprecision in the use of the two key concepts of solvability and index for DAEs. The index is also important in control and systems theory but with different terminology. The consideration of increasingly complex nonlinear DAEs makes a clear and correct development necessary. This paper will try to clarify several points concerning the index. After establishing some new and more precise terminology that we need, some inaccuracies in the literature will be corrected. The two types of indices most frequently used, the differentiation index and the perturbation index, are defined with respect to solutions of unperturbed problems. Examples are given to show that these indices can be very different for the same problem. We define new "maximum indices," which are the maxima of earlier indices in a neighborhood of the solution over a set of perturbations and show that these indices are simply related to each other. These indices are also related to an index defined in terms of Jacobians.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050165
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  • 3
    Electronic Resource
    Electronic Resource
    Constraint preserving integrators for general nonlinear higher index DAEs (1995)
    Springer
    Numerische Mathematik 69 (1995), S. 383-399 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 34A09, 65L05, 65H10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In the last few years there has been considerable research on numerical methods for differential algebraic equations (DAEs) $f(x', x, t) = 0$ where $f_{x'}$ is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three. Even in this case, the systems were often assumed to have a special structure. Recently a numerical method was proposed that could, in principle, be used to integrate general unstructured higher index solvable DAEs. However, that method did not preserve constraints. This paper will discuss a modification of that approach which can be used to design constraint preserving integrators for general nonlinear higher index DAEs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050099
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  • 4
    Electronic Resource
    Electronic Resource
    New developments in re-engineering organizations (1997)
    Bradford : Emerald
    The @international journal of productivity and performance management 46 (1997), S. 99-103 
    Details
    ISSN: 1741-0401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Economics
    Notes: Business process re-engineering was first popularized by Michael Hammer and James Champy, with their book, Reengineering the Corporation. The book advocated throwing away current business methods, models, procedures and processes and replacing them with newly re-engineered business processes. This and subsequent "re-engineering" methodologies have placed the primary focus on the business process, and put little, if any, emphasis on human factors. Suggests that many re-engineering projects fail because of this obvious neglect of human behavioural factors and identifies some proven management techniques which should be used in conjunction with any re-engineering methodology to ensure successful transformation of the business, and the people within the organization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/00438029710162953
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  • 5
    Electronic Resource
    Electronic Resource
    Linearization of DAEs along trajectories (1995)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 46 (1995), S. 70-84 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Over the last decade there has been a considerable amount of research on numerical and analytic aspects of linear and nonlinear differential algebraic equations (DAEs)F(x', x, t, u)=0. Many of these papers have either considered linear equations or based their analysis on linear equations. However, until very recently there has been little rigorous investigation of the relationship between the linearization of a DAE and the original equations. In this paper we carefully examine several aspects of this relationship. Positive results for time varying linearization and counter examples for time invariant linearization are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00952257
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  • 6
    Electronic Resource
    Electronic Resource
    Duality, observability, and controllability for linear time-varying descriptor systems (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 455-470 
    Details
    ISSN: 1531-5878
    Keywords: 34A08 ; 93B07 ; 93B15 ; 93C15 ; 93C50 ; Key words ; Descriptor ; Singular ; Differential-algebraic ; Observability ; Controllability ; Duality ; Structural forms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A characterization of observability for linear time-varying descriptor systemsE(t)x′(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x′(t)+F(t)x(t)=f(tt).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194883
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  • 7
    Electronic Resource
    Electronic Resource
    Progress on a general numerical method for nonlinear higher index DAEs II (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 123-138 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A method has been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit Runge-Kutta may not be appropriate. This method is based on solving nonlinear DAE derivative arrays. This paper discusses progress on the implementation of this method, resolves some of the issues involved, and lists some remaining problems. Computational experience on two prescribed path control problems is presented showing that the approach should prove practical for many applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188101
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  • 8
    Electronic Resource
    Electronic Resource
    Explicit formulae for completions of linear time varying singular systems of differential equations (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 185-199 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Completions of linear time varying singular systems of the formE(t)x′(t)+F(t)x′(t)=f(t) are explicitly computed using recent results on rational matrix functions. The algorithm and the theory behind it are carefully described. Computational issues are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188105
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  • 9
    Electronic Resource
    Electronic Resource
    Consistent initial conditions for singular nonlinear systems (1983)
    Springer
    Circuits, systems and signal processing 2 (1983), S. 45-55 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Conclusion A necessary condition for consistent initial conditions for singular nonlinear systems has been discussed. It is shown that for linear systems or systems of index less than three these conditions are equivlaent to previously reported results. However, for nonlinear systems of index greater than two these new conditions correct those previously reported. One consequence is that Euler's method may fail to estimate solutions for some semi-state equations. R. W. Newcomb's provision of an earlier version of [14] and subsequent correspondence is gratefully acknowledged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01598143
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  • 10
    Electronic Resource
    Electronic Resource
    Index two linear time varying singular systems of differential equations (1986)
    Springer
    Circuits, systems and signal processing 5 (1986), S. 97-107 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Linear time varying singular systems of differential equations of the formA(t)x′(t) + B(t)x(t)=f(t) whereA(t) is singular and the system has index at most two are considered. Recent results on their analytic solution are improved on. Examples are given that show these results are not easily extended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600189
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