Stability analysis for systems with saturation and backlash in the loop

This paper deals with the stability analysis problem for linear systems with saturation and backlash in the loop. The resulting system controlled by a static output feedback is a dynamical model with nested backlash and saturation operators. Uniform ultimate boundedness stability is tackled in a regional (local) or global context depending on the stability property of the open-loop system. Suitable regions of the state space in which the closed-loop trajectories can be captured are characterized, together with estimates of the basin of attraction of such regions. Convex optimization problems are proposed in order to give a constructive solution (in the sense of theoretical conditions associated to numerical procedures).