Stability analysis and design of a class of MIMO fuzzy control systems

摘要

This paper presents a new stability analysis method dedicated to a class of fuzzy control systems (FCSs) controlling multi input-multi output (MIMO) nonlinear processes by means of Takagi-Sugeno-Kang fuzzy logic controllers (FLCs). The stability analysis of the FCSs is carried out using LaSalle's global invariant set theorem by the separate stability analysis of each fuzzy rule in MIMO fuzzy control systems. Therefore the complexity of the stability analysis is reduced and the adding of new fuzzy rules can be conducted easily; this modification of FLC structure requires the fulfillment of only one of the conditions of the stability analysis theorem suggested in this paper. Another advantage of the stability analysis approach proposed in this paper is that the derivative of the Lyapunov function candidate must be only negative semi-definite in comparison with Lyapunov's stability theorem where it must be negative definite. The conservativeness of stability conditions is thus reduced, and this enables the convenient design of FLCs. The applicability and efficiency of the theoretical results are illustrated by numerical simulations for a representative MIMO process which deals with the level control in a three spherical tank system.