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Robust stabilization of uncertain switched non-linear systems subject to actuator saturation (2014)

Wei, Y., Lu, J., Li, Z.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-09-17

Beschreibung: This paper is concerned with the problem of robust stabilization for uncertain switched non-linear systems subject to actuator saturation and time-varying norm-bounded parameter uncertainties. Centred on the problem, a survey on both continuous and discrete-time domains has been made. The non-linearities in the state equations meet with the global Lipschitz conditions. In this paper, we are trying to work out a design of state feedback controllers and a state-dependent switching law so as to make the resulting closed-loop system robustly asymptotically stable at the origin with a large domain of attraction. Using the multiple Lyapunov functions method, some sufficient conditions for robust stabilization are derived. Furthermore, a group of static feedback controllers and a state-dependent switching law are designed, respectively, with an estimation of domain of attraction by solving a optimization problem, which are based on the solutions of certain linear matrix inequalities. Finally, a simulation example is presented to illustrate the effectiveness of the proposed results.

Print ISSN: 0265-0754

Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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Exponential stability of discrete-time recurrent neural networks with time-varying delays in the leakage terms and linear fractional uncertainties (2014)

Hu, M., Cao, J., Hu, A.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-09-17

Beschreibung: A class of discrete-time recurrent neural networks model is presented with the introduction of time-varying delays in the leakage terms and linear fractional uncertainties in parameters. The exponential stability analysis problem is studied, for the first time, for such kind of neural networks. In terms of linear matrix inequality approach, some delay-dependent stability criteria are established for the considered neural networks via a Lyapunov–Karasovskii functional. Three numerical examples are given to show the effectiveness of the theoretical results.

Print ISSN: 0265-0754

Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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3

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Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces (2014)

Liu, Z., Lv, J., Sakthivel, R.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-09-17

Beschreibung: Recently, the problem of approximate controllability has been extensively studied by many authors. However, up to now approximate controllability problems for fractional functional evolution inclusions with delay have not been considered in the literature. To fill this gap, this paper investigate the approximate controllability problem for fractional functional evolution inclusions in Hilbert spaces. The results are obtained under the corresponding linear system is approximately controllable. By using the fixed-point theorem for condensing multivalued maps and semigroup theory, sufficient conditions are formulated and proved. In the end, we give two examples to illustrate the application of the abstract results.

Print ISSN: 0265-0754

Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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4

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Attraction of stochastic neutral delay differential equations with Markovian switching (2014)

Li, B., Xu, D.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: In this paper, we investigate stochastic neutral delay differential equations with Markovian switching. By constructing an improved singular differential inequality and using some stochastic analysis techniques, we derive a sufficient criterion for ensuring the existence of the global attracting set and give a quantitative estimation with exponential decay form for solutions. Two numerical examples are discussed to illustrate the efficiency of the proposed method.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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5

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Distributed H{infty}-consensus filtering with sensor networks: a finite horizon solution (2014)

Shang, W., Kang, Y., Xi, H., Xia, Y., Zhao, Y.-B.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: The distributed H -consensus filtering problem is investigated for a class of discrete time-varying non-linear systems on a finite horizon. The topology of the sensor networks is assumed to be Markovian switching and the missing measurements (packet dropouts) problem is also considered. Based on the recursive linear matrix inequalities, an effective distributed H -consensus filter is designed, which is suitable for online computation. A numerical example is given to verify the effectiveness of the obtained results.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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6

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Swarm-based structure-specified controller design for bilateral transparent teleoperation systems via {mu} synthesis (2014)

Alfi, A., Khosravi, A., Lari, A.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: This paper proposes a novel robust controller design for bilateral teleoperation systems using μ synthesis based on an inspired algorithm namely particle swarm optimization with time-varying acceleration coefficients. In the proposed structure, the μ synthesis problem is considered as a constraint optimization problem. Indeed, this technique proposes a novel alternative solution for solving the μ synthesis problem to design simple structure controllers satisfying robust stability and performance. The goal of the proposed structure is to achieve complete transparency and robust stability for bilateral teleoperation systems with uncertainty in time delay and task environment. To this reason, two local controllers are designed. One local controller is responsible for tracking the master commands and the other local controller is in charge of force tracking as well as guaranteeing the stability of a closed-loop system. The comparative results demonstrate the effectiveness of the proposed controller compared with the results obtained from D-K iteration controller.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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7

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Super-stability and the spectrum of one-dimensional wave equations on general feedback controlled networks (2014)

Shang, Y., Liu, D., Xu, G.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: Two exact formulae for the eigenvalues of one-dimensional wave equations on general feedback controlled networks are presented. Especially, by them together with the exponential polynomial theory and the graph theory, it is shown that the oscillation of tree-shaped networks with one fixed vertex can rest in finite time with appropriate dampers. In the end, the two concrete networks are given and their eigenvalues are calculated to demonstrate our theoretical results.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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Reconstructing the potential for the one-dimensional Schrodinger equation from boundary measurements (2014)

Avdonin, S. A., Mikhaylov, V. S., Ramdani, K.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: We consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. We use the boundary control method to recover the spectrum of the problem from the observation at either left or right endpoints. Using the specificity of the one-dimensional situation, we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only a finite number of eigenvalues are known and prove the convergence of the method.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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9

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Simultaneous controller design for a class of time-varying linear systems (2014)

Yu, T., Guo, H.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: In this paper, we establish the parametrization of simultaneously stabilizing controllers for a class of time-varying linear systems within the framework of nest algebras. A new approach to the simultaneous stabilization of three time-varying linear systems is also provided.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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10

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Asymptotic stability of diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes and nonlocal time delays (2014)

Tian, Y., Weng, P.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2014-03-18

Beschreibung: A diffusive predator–prey model with nonlocal time delays is considered in the present paper. We establish the nonexistence of nonconstant steady states by the use of the auxiliary functions. We also study the convergence of the solution by using the method of upper and lower solutions. The sufficient conditions we obtained are simple and easily verifiable.

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Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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