H∞ fuzzy PID control for discrete time-delayed T-S fuzzy systems

Abstract

Abstract This paper is concerned with the H∞ fuzzy proportional-integral-derivative (PID) control problem for delayed Takagi–Sugeno (T-S) fuzzy systems in the discrete-time setting. Based on the current and historical measurement data, a novel T-S fuzzy PID controller is developed with which the integral-loop is generated based on a fixed number of past measurements for the purpose of reducing the computational burden, where a special augmentation scheme is adopted to simplify the closed-loop system. The aim of this paper is to design the PID controller parameters such that the closed-loop T-S fuzzy system is exponentially stable and the prescribed H∞ disturbance attenuation performance is achieved. By adopting the Lyapunov stability theory and the linear matrix inequality technology, sufficient conditions are obtained for the existence of the desired fuzzy PID controllers. In addition, an iterative optimization procedure is proposed to design the controller parameters according to the cone complementarity linearization algorithm. Finally, a numerical simulation example is exploited to demonstrate the usefulness and effectiveness of our proposed design scheme.