Ultimate boundedness of discrete stochastic time-delay systems with logic impulses

In this article, we investigate the role of Lyapunov functions in evaluating nonlinear-nonquadratic cost functionals for Itô-type nonlinear stochastic difference equations. Specifically, it is shown that the cost functional can be evaluated in closed-form as long as the cost functional is related in a specific way to an underlying Lyapunov function that guarantees asymptotic stability in probability. This result is then used to analyze discrete-time linear as well as nonlinear stochastic dynamical systems with polynomial and multilinear cost functionals. Furthermore, a stochastic optimal control framework is developed by exploiting connections between stochastic Lyapunov theory and stochastic Bellman theory. In particular, we show that asymptotic and geometric stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady state form of the stochastic Bellman equation, and hence, guaranteeing both stochastic stability and optimality.

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“…Finally, extensions to stochastic systems with time delays and impulsive effects will also be explored. 31…”

Section: Discussionmentioning

confidence: 99%

Nonlinear–nonquadratic optimal and inverse optimal control for discrete‐time stochastic dynamical systems

Lanchares

Haddad

2021

Intl J Robust & Nonlinear

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“…In addition, boundedness of SDSs is also an important topic. For example,

(μ, ρ)

‐ultimate boundedness of discrete stochastic time‐delay system 4 was studied. Besides, He and Huang 5 investigated the ultimate boundedness analysis of SDSs with Markov jump parameters.…”

Section: Introductionmentioning

confidence: 99%

Stochastic stability and stabilization for stochastic differential semi‐Markov jump systems with incremental quadratic constraints

Zhang

Huang

Zhang

2021

Intl J Robust & Nonlinear

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The problem of the stochastic stability analysis and state feedback stabilization for nonlinear stochastic differential semi‐Markov jump systems with incremental quadratic constraints is investigated in this article. Different from Markovian process, the transition rate is time varying with known bounds and the sojourn time is conformed to the Weibull distribution in semi‐Markov process. Traditional nonlinear constraint such as Lipschitz, one‐sided Lipschitz, and so forth, is extended to incremental quadratic constraint. By the mode‐dependent Lyapunov function and the slack variable method, the sufficient conditions ensuring that the considered systems are stochastically stable are formulated by linear matrix inequalities. Then, a state feedback controller is designed to drive the closed‐loop system stochastically stable. Finally, an example of helicopter is used to illustrate the superiority as well as effectiveness of the results in this treatise.

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Stability analysis of time-delay discrete systems with logic impulses

2019

Communications in Nonlinear Science and Numerical Simulation

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Ultimate boundedness of discrete stochastic time-delay systems with logic impulses

Cited by 4 publications

References 39 publications

Nonlinear–nonquadratic optimal and inverse optimal control for discrete‐time stochastic dynamical systems

Nonlinear–nonquadratic optimal and inverse optimal control for discrete‐time stochastic dynamical systems

Stochastic stability and stabilization for stochastic differential semi‐Markov jump systems with incremental quadratic constraints

Stability analysis of time-delay discrete systems with logic impulses

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