Performance analysis and extended dissipative controller design for Itô stochastic-delayed IT2 fuzzy models

Abstract

This paper deals with the problems of stochastic asymptotic stability analysis and extended dissipativity as well as controller design for Itô stochastic-delayed IT2 fuzzy systems by using line integral type Lyapunov–Krasovskii functional (LKF). A good estimate of the upper bound for the line integral type LKF is achieved, based on which, the conditions of stochastic asymptotic stability and extended dissipativity are derived. A comparison has been drawn between the conditions derived by line integral type LKF and the ones by the quadratic LKF in a numerical example, to indicate that the conditions by line integral approach are more general than the ones via quadratic method. Meanwhile, these conditions are of nonlinear form with respect to some matrix variables which makes the determination of the extended dissipative controller difficult. Inspired by cone complementarity linearisation algorithm and a novel matrix decoupling method, the state feedback controller is developed by transforming the nonlinear matrix inequalities into a quadratic optimisation problem with linear matrix inequality constraints. Finally, two examples are given to show the validity of our proposed approach.

Keywords:

• Extended dissipativity
• IT2 fuzzy model
• Itô stochastic delayed system
• line integral type Lyapunov-Krasovskii functional
• quadratic optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of P.R. China [grant numbers 61673149, 61333009, U1509205], and the National Natural Science Foundation of Zhejiang Province [grant number LZ12F03001].

Notes on contributors

Yingying Han

Yingying Han received the B.Sc.degree in mathematics from Huaibei Normal University, Huaibei, China, in 2014. She received the M.Sc.degree in Operational Research and Cybernetics from Hangzhou Dianzi University, Hangzhou, China, in 2017. Her research interests are in nonlinear systems,fuzzy systems, robust control and filtering, stochastic analysis.

Shaosheng Zhou

Shaosheng Zhou received the M.Sc. degree in applied mathematics from Qufu Normal University, Shandong, in 1996, and the Ph.D. degree in control theory and application from Southeast University in 2001, respectively. He was a Research Associate with the Department of Manufacturing Engineering and Engineering management, the City University of Hong Kong, from January 2000 to July 2000 and from November 2001 to June 2002. From October 2002 to January 2003 and November 2004 to April 2005, he was a Research Associate with the Department of Mechanical Engineering, the University of Hong Kong. He also worked as a research fellow with the School of Quantitative Methods and Mathematical Science, the University of Western Sydney, Australia, from September 2005 to February 2006. He is currently a full Professor with the Department of Automation, Hangzhou Dianzi University, and has coauthored more than 80 journal papers. His research interests are in nonlinear systems, robust control and filtering, fuzzy control, stochastic analysis.