Equilibrium stability of a nonlinear structural switching system with actuator delay

Abstract

In this paper, a Lyapunov–Krasovskii functional is used to obtain sufficient conditions of asymptotic stability for the equilibrium of a nonlinear feedback system with state-dependent uncontrolled switching, herein called structural switching, and with actuator delay. The solution of the problem is addressed in two steps. First, a predictive feedback method is used to compensate the actuator delay of the associated linearized system. Thus, the time-delayed control is replaced with a state delay, and the effect of the control appears in a non-homogeneous term in the linearized system. Second, a theorem of asymptotic stability of equilibrium is obtained for the nonlinear switched system, whose linearized components were considered separately in the first step. The result is also valid for certain problems of state-dependent controlled switching. The numerical application, done on a consecrated real world system, the electrohydraulic servomechanism, highlights real difficulties, which are usually avoided by academic constructs in which the results are sometimes illustrated on insignificant models, represented, for example, by 2 × 2 didactic matrices.