Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems

Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems

This paper studies robust stability, stabilization, and H∞ control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust H∞ state feedba...

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Main Authors: Tianliang Zhang, Yu-Hong Wang, Xiushan Jiang, Weihai Zhang
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/5185784
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spelling doaj-62a4cd5185634f80bc243a6604f24ecc2020-11-25T00:29:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/51857845185784Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic SystemsTianliang Zhang0Yu-Hong Wang1Xiushan Jiang2Weihai Zhang3College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, Shandong 266510, ChinaCollege of Information and Control Engineering, China University of Petroleum (East China), Qingdao, Shandong 266510, ChinaCollege of Information and Control Engineering, China University of Petroleum (East China), Qingdao, Shandong 266510, ChinaCollege of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, ChinaThis paper studies robust stability, stabilization, and H∞ control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust H∞ state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust H∞ performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.http://dx.doi.org/10.1155/2016/5185784
collection DOAJ
language English
format Article
sources DOAJ
author Tianliang Zhang
Yu-Hong Wang
Xiushan Jiang
Weihai Zhang
spellingShingle Tianliang Zhang
Yu-Hong Wang
Xiushan Jiang
Weihai Zhang
Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
Mathematical Problems in Engineering
author_facet Tianliang Zhang
Yu-Hong Wang
Xiushan Jiang
Weihai Zhang
author_sort Tianliang Zhang
title Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
title_short Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
title_full Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
title_fullStr Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
title_full_unstemmed Robust Stability, Stabilization, and H∞ Control of a Class of Nonlinear Discrete Time Stochastic Systems
title_sort robust stability, stabilization, and h∞ control of a class of nonlinear discrete time stochastic systems
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description This paper studies robust stability, stabilization, and H∞ control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust H∞ state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust H∞ performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.
url http://dx.doi.org/10.1155/2016/5185784
work_keys_str_mv AT tianliangzhang robuststabilitystabilizationandhcontrolofaclassofnonlineardiscretetimestochasticsystems
AT yuhongwang robuststabilitystabilizationandhcontrolofaclassofnonlineardiscretetimestochasticsystems
AT xiushanjiang robuststabilitystabilizationandhcontrolofaclassofnonlineardiscretetimestochasticsystems
AT weihaizhang robuststabilitystabilizationandhcontrolofaclassofnonlineardiscretetimestochasticsystems
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