Robust polytopic invariant sets for discrete fuzzy control systems

TS fuzzy models are exact representations of nonlinear systems in a compact zone (sector nonlinearity). Once a controller is found by Lyapunov methods, determining the set of initial conditions such that the state does not leave the modelling region is an important problem to be solved. Also, determining the set to which the disturbances will steer the system is also necessary to ensure that the size of the modelling region has been correctly estimated. This paper proposes polytopic approximation to such sets based in algorithms from [1]. A Polya-based approach has been introduced in order to (conservatively) transform the nonlinear invariant set problem into a polytopic one.