Stability analysis of discrete-time fuzzy-model-based control systems with time delay: Time delay-independent approach

This paper presents the stability analysis of discrete-time fuzzy-model-based control systems with time delays. To facilitate the stability analysis, the T–S fuzzy model is employed to represent the discrete-time nonlinear system. Due to the multiplication property of the fuzzy-model-based control system, the number of LMI-based stability conditions is p(p+1)/2 where p is the number of rules for the fuzzy model and fuzzy controller. Consequently, the computational demand for solving the solution to the stability conditions is very expensive, especially when the value of p is large. The problem becomes much worse when the relaxed stability conditions are formulated as huge matrices. The huge matrices incorporate the information of all the closed-loop subsystems, which may cause the solution of the LMI-based stability conditions difficult or even impossible to obtain owing to the limited computer power. In this paper, to reduce the computational demand, the fuzzy-model-based control system is divided into parts which the control input will handle separately. As a result, the multiplication property of the fuzzy-model-based control system can be removed, which effectively reduces the number of stability conditions to p and the computational demand for finding the solution can be reduced. LMI-based delay-independent stability conditions are derived using the Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed approach.