Abstract
Abstract We propose a numerical method to compute stabilizing state feedback control laws and associated polyhedral invariant sets for nonlinear systems represented by Fuzzy Takagi-Sugeno (T-S) models, subject to state and control constraints, and persistent disturbances. Sufficient conditions are derived under which a given polyhedral set is positively invariant under a Parallel Distributed Compensation (PDC), in the form of bilinear algebraic inequalities. Then, a bilinear programming (BP) problem is proposed to compute the state feedback gains and an associated positively invariant polyhedron, with predefined complexity, which solve a constrained regulation problem for the Fuzzy T-S system. A numerical example illustrates the effectiveness of the method.
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