Stability analysis for switched systems with continuous-time and discrete-time subsystems: a Lie algebraic approach

@article{Zhai2004StabilityAF,
  title={Stability analysis for switched systems with continuous-time and discrete-time subsystems: a Lie algebraic approach},
  author={Guisheng Zhai and Derong Liu and Joe Imae and Tomoaki Kobayashi},
  journal={Proceedings of the 2004 American Control Conference},
  year={2004},
  volume={5},
  pages={4555-4560 vol.5}
}
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. A numerical example is provided to demonstrate the result.