Improved LMI Conditions for Local Quadratic Stabilization of Constrained Takagi–Sugeno Fuzzy Systems

This paper is devoted to the control synthesis of constrained Takagi–Sugeno (T–S) fuzzy systems. These systems are subject to multiple constraints, namely actuator saturation, system state constraints, and also $${\mathcal {L}}_2$$L2-disturbances. Using descriptor redundancy approach, new design conditions guaranteeing the existence of an input-saturated parallel distributed state feedback compensator are formulated as an LMI optimization problem with extra matrix decision variables. Differently from most of results dealing with the same local control context of constrained T–S systems, a generalized sector condition is used to handle effectively the nonlinearity of the control input. The use of a descriptor redundancy representation in conjunction with a sector condition for actuator saturation allows to reduce significantly the design conservatism while keeping a simple control structure. The effectiveness of the proposed method compared to many recent works is clearly demonstrated by means of numerical examples.