Ultimate bounded stability and stabilization of linear systems interconnected with generalized saturated functions

Abstract

This paper proposes some ultimate bounded stability analysis and stabilization conditions for systems involving actuators with different nonlinear elements, like for instance both saturation and dead-zone or both saturation and stick–slip. Results are based on the use of a convex differential inclusion approach. Indeed, an adequate property allowing to upper-bound some product terms related to the nonlinearity is provided. Thus, constructive conditions associated to convex optimization schemes are developed to determine suitable regions of the state space in which the closed-loop trajectories can be captured.