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

Guisheng Zhai; Xuping Xu; Hai Lin; Derong Liu

International Journal of Applied Mathematics and Computer Science (2007)

- Volume: 17, Issue: 4, page 447-454
- ISSN: 1641-876X

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topZhai, Guisheng, et al. "Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 447-454. <http://eudml.org/doc/207849>.

@article{Zhai2007,

abstract = {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.},

author = {Zhai, Guisheng, Xu, Xuping, Lin, Hai, Liu, Derong},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {exponential stability; switched systems; arbitrary switching dwell time scheme; Lie algebra; common quadratic Lyapunov functions; arbitrary switching; dwell time scheme},

language = {eng},

number = {4},

pages = {447-454},

title = {Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems},

url = {http://eudml.org/doc/207849},

volume = {17},

year = {2007},

}

TY - JOUR

AU - Zhai, Guisheng

AU - Xu, Xuping

AU - Lin, Hai

AU - Liu, Derong

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2007

VL - 17

IS - 4

SP - 447

EP - 454

AB - 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.

LA - eng

KW - exponential stability; switched systems; arbitrary switching dwell time scheme; Lie algebra; common quadratic Lyapunov functions; arbitrary switching; dwell time scheme

UR - http://eudml.org/doc/207849

ER -

## References

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