Polyhedral Regions of Robust Local Stability for Linear Systems With Saturating Controls

Abstract The estimation of regions of robust local asymptotic stability of uncertain discrete-time linear systems with saturating control inputs is performed constructing robustly contractive polyhedral sets. New necessary and sufficient conditions for compact polyhedral sets be robustly contractive are derived. Based on linear programming formulation of these conditions, an effective non nomothetic expansion procedure is proposed for construction of robustly contractive potyhedral sets and consequent estimation of regions of robust local asymptotic stability of closed-loop saturated systems. The procedure starts with the supremal robustly contractive potyhedral set contained in the region of linear control arid progressively expands it over the region of nonlinear saturated control.