Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

Deng, Jian

doi:10.1155/2018/4725148

Cited by 3 publications

(1 citation statement)

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“…Moment stability means the stability of probability under the condition of linear growth (Possieri and Teel, 2017). Most of the available research studies have focused on the second-order moment stability (Briat, 2016; Chen and Zheng, 2016; Deng, 2018; Mao et al, 2014). In fact, for real engineering systems, security is a very important property, and probability convergence is the most appropriate type because the corresponding stability property, namely, probability stability, ensures that all sample paths converge to the equilibrium point with probability one.…”

Section: Introductionmentioning

confidence: 99%

Constrained regulation problem for continuous-time stochastic systems under state and control constraints

Yang

2021

Journal of Vibration and Control

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Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.

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