Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems
Tadeusz Kaczorek, Przemysław Przyborowski (2009)
Control and Cybernetics
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Tadeusz Kaczorek, Przemysław Przyborowski (2009)
Control and Cybernetics
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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.
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.
Tadeusz Kaczorek (2010)
International Journal of Applied Mathematics and Computer Science
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The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one,...
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.
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...
Long Wang (2004)
Control and Cybernetics
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Tadeusz Kaczorek (2005)
International Journal of Applied Mathematics and Computer Science
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The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.