Displaying similar documents to “New stability conditions for positive continuous-discrete 2D linear systems”

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Mikołaj Busłowicz, Andrzej Ruszewski (2012)

International Journal of Applied Mathematics and Computer Science

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Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Independence of asymptotic stability of positive 2D linear systems with delays of their delays

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

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It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.

Robust stability of positive continuous-time linear systems with delays

Mikołaj Busłowicz (2010)

International Journal of Applied Mathematics and Computer Science

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The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

Positive 2D discrete-time linear Lyapunov systems

Przemysław Przyborowski, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

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Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

Guisheng Zhai, Xuping Xu (2010)

International Journal of Applied Mathematics and Computer Science

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We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions...

The choice of the forms of Lyapunov functions for a positive 2D Roesser model

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

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The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.