Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

This paper investigates exponentially stable guaranteed cost control (GCC) for a class of nonlinear systems which is represented by Takagi–Sugeno (T–S) fuzzy systems. State feedback controllers of parallel distributed compensation (PDC) structure are designed by the means of GCC for continuous and discrete-time T–S fuzzy systems respectively. GCC methods in this paper adopt quadratic performance functions, which take effects of control efforts, regulation errors and convergence rates into consideration simultaneously, to provide desirable performance and fast response for closed-loop systems. Sufficient design conditions that guarantee exponential stabilities of resulting closed-loop systems with predefined convergence rates are presented. By setting different convergence rates, response speed of the closed-loop nonlinear system can be adjusted. The proposed design procedures are eventually converted into linear matrix inequalities (LMIs) problems of minimizing upper bounds of the guaranteed cost functions. Finally, a well-known nonlinear benchmark control example and a truck–trailer example demonstrate the effectiveness and feasibility of all the proposed methods.