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3 International Journal of Applied Mathematics and Computer Science

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

100%

Zhai G. , Xu X.

nr 2

249-259

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.

Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

80%

Zhai G. , Xu X. , Lin H. , Liu D.

tom 17

nr 4

447-454

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.

Hybrid stabilization of discrete-time LTI systems with two quantized signals

70%

Zhai G. , Matsumoto Y. , Chen X. , Imae J. , Kobayashi T.

nr 4

509-516

We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.