Abstract
The determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a perturbed linear system. From this representation, a necessary and sufficient algebraic condition relative to the positive invariance of a polyhedral set is given. In a second stage, a necessary and sufficient condition to the contractivity of such a positively invariant set is stated. Consequently, the polyhedral set can be associated to a Lyapunov function and the local asymptotic stability of the saturated closed-loop system inside the set is guaranteed. An algorithm based on linear programming is proposed to generate homothetic expansions of a positively invariant and contractive polyhedral set w.r.t. closed-loop saturated system.
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