Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems: A Lie Algebraic Approach

2005 ◽  
Author(s):  
Guisheng Zhai ◽  
Derong Liu ◽  
J. Imae ◽  
T. Kobayashi
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Switched Systems ◽  
Algebraic Approach

scholarly journals Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

2007 ◽  
Vol 17 (4) ◽  
pp. 447-454 ◽  
Author(s):  
Guisheng Zhai ◽  
Xuping Xu ◽  
Hai Lin ◽  
Derong Liu
Keyword(s):  
Stability Analysis ◽  
Lie Algebra ◽  
Discrete Time ◽  
Continuous Time ◽  
Switched Systems ◽  
Switched System ◽  
Quadratic Lyapunov Function ◽  
Algebraic Stability ◽  
Arbitrary Switching ◽  
Exponentially Stable

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time SubsystemsWe 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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