Global stability for systems with nested backlash and saturation operators

This paper is concerned with the problem of stability analysis for a certain class of nonlinear systems resulting from nested backlash and saturation operators. Constructive conditions in LMI form to ensure the global stability of the system, are proposed by using some suitable Lyapunov functional, generalized sector conditions and a polytopic representation. Such global stability conditions impose the presence of an additional feedback between the output and the input of the nonlinear element. The associated gain is then fixed by construction. This additional gain can allow, as in the anti-windup context, to mitigate the unwished behavior of the nonlinear elements. The envelope of the associated set of all the admissible equilibrium points is computed.