Smoothing switched control for uncertain T-S fuzzy systems with unknown membership functions, actuator saturation and disturbance

This paper proposes conditions that ensure local ultimate bounded stability for nonlinear systems constrained to a region of operation, subject to actuator saturation and persistent norm-bounded disturbance. The nonlinear plant is described by an uncertain Takagi-Sugeno (T-S) fuzzy model with unknown membership functions and two control laws (switched control and smooth switched control) are proposed. The designs of the gains and decision matrices used in the control laws are based on Linear Matrix Inequalities (LMIs) and use a line search procedure. The project also provides an invariant region in which for all initial condition inside it the local ultimate bounded stability is ensured. The proposed design also allows specifying a polytope of initial conditions that must belong to the invariant region of initial conditions. The theoretical results are illustrated by simulation results in a ball-and-beam system.