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

100%
Zhai G., Xu X.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 2
249-259
EN
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 of the existing results for switched linear state space systems.
2
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Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

81%
Zhai G., Xu X., Lin H., Liu D.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 4
447-454
EN
We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.
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