Stability theory of hybrid dynamical systems with time delay

@article{Liu2006StabilityTO,
  title={Stability theory of hybrid dynamical systems with time delay},
  author={Xinzhi Liu and Jianhua Shen},
  journal={IEEE Transactions on Automatic Control},
  year={2006},
  volume={51},
  pages={620-625}
}
By defining the bounded time lag space and other related concepts, this note formulates the notion of hybrid dynamical systems with time delay, which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis. It also investigates stability properties of invariant sets by the method of Lyapunov functions and the Razumihin techniques. Criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with… CONTINUE READING

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  • 2018
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References

Publications referenced by this paper.
SHOWING 1-10 OF 12 REFERENCES

Stability analysis of a class of hybrid dynamic systems

X. Liu, X. Shen, Y. Zhang
  • Dyna. Contin. Discrete Imp. Syst., ser. B, vol. 8, pp. 359–373, 2001.
  • 2001
VIEW 1 EXCERPT

Recent trends in the stability analysis of hybrid dynamical systems

A. N. Michel
  • IEEE Trans. Autom. Control, vol. 45, no. 1, pp. 120–134, Jan. 1999.
  • 1999
VIEW 1 EXCERPT

Impulsive hybrid systems and stability theory

V. Lakshmikantham, X. Liu
  • Dyna. Syst. Appl., vol. 7, pp. 1–9, 1998.
  • 1998
VIEW 1 EXCERPT

Stability analysis of systemswith impulsive effects

  • IEEE Trans. Autom. Control, vol. 43, no. 12, pp. 1719–1723, Dec. 1998.
  • 1998

Qualitative Theory of Dynamical Systems

A. N. Michel, K. Wang
  • 1995
VIEW 1 EXCERPT