Polyhedral Robust Asymptotic Stability Regions of Discrete-Time Linear Systems with Saturating Controls

Abstract The estimation of the region of robust local asymptotic stability of uncertain discrete-time linear systems with saturating control inputs is performed constructing piecewise-affine Lyapunov functions. New necessary and sufficient conditions for piecewise-affine functions be Lyapunov functions are derived. Based on linear programming formulation of these conditions, an effective non homothetic expansion procedure is proposed for construction of such Lyapunov functions for estimation of the region of robust local asymptotic stability of closed-loop saturating systems. The results obtained are strictly less conservative than those obtained via construction of contractive polyhedral sets associated to Minkowski Lyapunov functions.