Nonfragile Dissipative Fuzzy PID Control With Mixed Fading Measurements

Abstract

This article is concerned with the extended dissipative fuzzy proportional–integral–derivative (PID) control problem for nonlinear systems subject to controller parameter perturbations over a class of mixed fading channels. The sensors of plant are divided into two groups according to engineering practice, where the individual sensor group transmits the measurements to the controller via a respective communication channel undergoing specific fading effects. Considering the complicated nature of the signal fading with the transmission channels, two stochastic models (i.e., the independent and identically distributed fading model and the Markov fading model) are simultaneously employed to describe the mixed fading effects of the two communication channels corresponding to the two sensor groups. The objective of this article is to design a nonfragile PID controller such that the closed-loop system is exponentially stable in mean square and extended stochastically dissipative. With the assistance of the Lyapunov stability theory and stochastic analysis method, sufficient conditions are obtained to analyze the system performance. Then, within the established theoretical framework, an iterative optimization algorithm is proposed to design the desired controller parameters by using the convex optimization technique. Finally, two simulation examples are given to verify the effectiveness of the proposed control schemes.