Robust reliable \(H_{\infty}\) control for nonlinear stochastic Markovian jump systems
type: Item
instance of: scholarly article
title: Robust reliable \(H_{\infty}\) control for nonlinear stochastic Markovian jump systems
zbMATH Open document ID: 1264.93259
DOI: 10.1155/2012/431576
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: The robust reliable \(H_{\infty}\) control problem for a class of nonlinear stochastic Markovian jump systems (NSMJSs) is investigated. The system under consideration includes Itô-type stochastic disturbance, Markovian jumps, as well as sector-bounded nonlinearities and norm-bounded stochastic nonlinearities. Our aim is to design a controller such that, for possible actuator failures, the closed-loop stochastic Markovian jump system is exponential mean-square stable with convergence rate \(\alpha\) and disturbance attenuation \(\gamma\). Based on the Lyapunov stability theory and Itô differential rule, together with LMIs techniques, a sufficient condition for stochastic systems is first established in Lemma 3. Then, using the lemma, the sufficient conditions of the solvability of the robust reliable \(H_{\infty}\) controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 6173281
Wikidata QID: Q58911650
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/431576
OpenAlex ID: W2042396750
cites work: Robust high moment stabilizing control for stochastic systems with jumps.
cites work: Stability of stochastic differential equations with Markovian switching
cites work: On hybrid control of a class of stochastic non-linear Markovian switching systems
cites work: Reliable \(H_\infty\) controller design for linear systems
cites work: Robust reliable \(H_\infty \) control for uncertain nonlinear systems via LMI approach
cites work: Reliable dissipative control for stochastic impulsive systems
cites work: Reliable \(H_\infty \) control for discrete-time piecewise linear systems with infinite distributed delays
cites work: State Feedback $H_\infty$ Control for a Class of Nonlinear Stochastic Systems
cites work: Robust H/sub /spl infin// filtering for nonlinear stochastic systems
cites work: Reliable \(H_{\infty }\) filtering for discrete time-delay systems with randomly occurred nonlinearities via delay-partitioning method
cites work: Reliable H∞ filtering for discrete time-delay Markovian jump systems with partly unknown transition probabilities
cites work: Stochastic faulty actuator-based reliable control for a class of interval time-varying delay systems with Markovian jumping parameters
cites work: Robust reliable control for discrete-time-delay systems with stochastic nonlinearities and multiplicative noises
cites work: Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching
cites work: \(H_\infty\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities
cites work: Absolute stability of time-delay systems with sector-bounded nonlinearity
cites work: \(\mathcal H_\infty\) and \(\mathcal L_2/\mathcal L_\infty\) model reduction for system input with sector nonlinearities
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: H∞ estimation for discrete‐time linear uncertain systems
description: scientific article; zbMATH DE number 6173281