Displaying similar documents to “Independence of asymptotic stability of positive 2D linear systems with delays of their delays”

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.

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 realization problem for positive continuoustime systems with reduced numbers of delays

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

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A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.

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.

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...

Positive partial realization problem for linear discrete-time systems

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

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A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

New stability conditions for positive continuous-discrete 2D linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

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New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

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The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.