Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic

Abstract

This paper deals with the design of stable rule-based fuzzy control systems. Interval analysis is applied to design a stable fuzzy Takagi–Sugeno–Kang controller using a robust condition to ensure the stability. The presented methodology starts with a state model of the plant, finds a candidate fuzzy controller and uses an interval arithmetic algorithm to verify the stability of closed-loop fuzzy model. It is important to emphasize the generality of the presented methodology for fuzzy controller synthesis since there are no constraints in the state vector nor in the control vector. This methodology can also be used with nonlinear plant models. In previous works we showed the applicability of the interval analysis to design a controller that ensures the stability of first order nonlinear system. In this paper, we extend the analysis and the synthesis of stable fuzzy control system to the multivariable case. An example with a fuzzy controller for a nonlinear system is presented to illustrate the design procedure.