Simple conditions for robust stability of positive discrete-time linear systems with delays
Mikołaj Busłowicz (2010)
Control and Cybernetics
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Mikołaj Busłowicz (2010)
Control and Cybernetics
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Soo R. Lee, Mohamad Jamshidi (1992)
Kybernetika
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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.
Yeong-Jeu Sun (2005)
Control and Cybernetics
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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...
Keqin Gu (2001)
Kybernetika
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This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov–Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple...
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.