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

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4 Author(s)
Zhai, Guisheng ; Dept. of Mech. Eng., Osaka Prefecture Univ., Japan ; Derong Liu ; Imae, J. ; Kobayashi, T.

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 continuous-time subsystems are Hurwitz stable, all discrete-time subsystems are Schur stable, and furthermore the obtained 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. A numerical example is provided to demonstrate the result.

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Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:53 ,  Issue: 2 )