Indefinite multiple Lyapunov functions of p th moment input‐to‐state stability and p th moment integral input‐to‐state stability for the nonlinear time‐varying stochastic systems with Markovian switching

2021 ◽  
Author(s):  
Qian Liu ◽  
Yong He ◽  
Chongyang Ning
Keyword(s):  
Lyapunov Functions ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Time Varying ◽  
Multiple Lyapunov Functions ◽  
Moment Integral

Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

2018 ◽  
Vol 41 (2) ◽  
pp. 350-365 ◽  
Author(s):  
Xin Zhang ◽  
Huashan Liu ◽  
Yiyuan Zheng ◽  
Yuqing Sun ◽  
Wuneng Zhou ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Systems ◽  
Transition Probabilities ◽  
Time Varying ◽  
Analysis Method ◽  
Multiple Lyapunov Functions ◽  
Time Varying Delay ◽  
Neutral Stochastic Systems ◽  
Varying Delay

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

scholarly journals H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Lijun Gao ◽  
Yuqiang Wu
Keyword(s):  
Stochastic Systems ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Markovian Switching ◽  
Time Varying ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Integral Sliding Surface ◽  
The Given

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

Pth moment input-to-state stability of stochastic impulsive switched delayed systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3468-3476
Author(s):  
Lijun Gao ◽  
Shengyan Wang
Keyword(s):  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Delayed Systems ◽  
Stable Function ◽  
Exponentially Stable ◽  
Delayed System ◽  
The Relationship ◽  
Delayed Impulses ◽  
Moment Integral

This paper investigates the pth moment input-to-state stability (ISS) and the pth moment integral input-to-state stability (iISS) of stochastic impulsive switched delayed system with delayed impulses. By employing the method of multiple Lyapunov-Krasovskii functionals and the uniformly exponentially stable function, some relaxed Krasovskii-type sufficient conditions ensuring the pISS/piISS of the addressed systems are developed. These conditions imply the relationship among the impulsive frequency, the time delay existing in impulses, and the coefficients of the estimated upper bound for the derivative of a Lyapunov function. It is shown that if the continuous stochastic delayed dynamics is ISS, and the impulsive effects are destabilizing, then the stochastic impulsive switched delayed system is ISS with respect to the relationship. Compared with the existing results, the conditions obtained results have three relaxations, that is, the derivative of Lyapunov functions of subsystems are allowed to be sign-changing time-varying function rather than a negative definite constant, all subsystems are allowed to be unstable, and the effect of delayed impulses are considered. Finally, an example is provided to illustrate the effectiveness of the results.

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