Vector-Lyapunov-Function-Based Input-to-State Stability of Stochastic Impulsive Switched Time-Delay Systems

In this paper, the input-to-state stability is studied for stochastic impulsive switched time-delay systems. Using the vector Lyapunov function, average dwell time, and the properties of M-matrix, different types of sufficient conditions are established. Both the case that the continuous dynamics is...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2019-02, Vol.64 (2), p.654-669
Main Authors: Ren, Wei, Xiong, Junlin
Format: Article
Language:English
Subjects:
Dwell time
Dynamic stability
Hybrid system
impulsive system
input-to-state stability (ISS)
Liapunov functions
Lyapunov methods
Numerical stability
Stability criteria
stochastic systems
switched system
Switched systems
Switches
Synchronism
Thermal stability
Time delay systems
time-delay system
vector Lyapunov functions
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Summary:In this paper, the input-to-state stability is studied for stochastic impulsive switched time-delay systems. Using the vector Lyapunov function, average dwell time, and the properties of M-matrix, different types of sufficient conditions are established. Both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed, and the stability conditions are obtained. In the obtained stability conditions, different components of the vector Lyapunov function are allowed to be coupled; the information in consecutive impulsive switching intervals is also allowed to be coupled. Therefore, the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results. Furthermore, we investigate the relationships among the vector Lyapunov function approach, the approach based on the comparison principle and the scalar Lyapunov function approach. According to the vector Lyapunov function, the comparison system is constructed and the scalar-Lyapunov-function-based stability conditions are established. Finally, the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos-based secure communication systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2836191