Delay-Dependent Guaranteed Cost Control for Uncertain Stochastic Fuzzy Systems With Multiple Time Delays

• Published in: IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 38; no. 1; pp. 126 - 140
• Main Authors: Zhang, Huaguang, Wang, Yingchun, Liu, Derong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2008
• Subjects: Algorithms; Computer Simulation; Control systems; Cost function; Cybernetics; Delay dependence; Delay effects; Dynamical systems; Feedback; Fuzzy; Fuzzy control; Fuzzy Logic; Fuzzy systems; guaranteed cost control; Linear matrix inequalities; linear matrix inequality (LMI); Matrices; Models, Statistical; multiple time delays; Nonlinear control systems; Nonlinear systems; stochastic fuzzy systems; Stochastic Processes; Stochastic systems; Stochasticity; Takagi-Sugeno model; Time delay; Time Factors; linear matrix inequality (LMI); guaranteed cost control; Delay dependence; multiple time delays; stochastic fuzzy systems
• ISSN: 1083-4419; 1941-0492
• DOI: 10.1109/TSMCB.2007.910532

This paper studies the guaranteed cost control problem for a class of uncertain stochastic nonlinear systems with multiple time delays represented by the Takagi-Sugeno fuzzy model with uncertain parameters. By constructing a new stochastic Lyapunov-Krasovskii functional, sufficient conditions for delay-dependent guaranteed cost control are obtained which do not require system transformation or relaxation matrices. Conditions for the existence of an optimal guaranteed cost controller are presented in the linear matrix inequality format. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper.