Backstepping-based delayed impulsive control for input-to-state stabilization of disturbed electrohydraulic servo systems

This paper investigates the input-to-state stability (ISS) of disturbed electrohydraulic servo systems (EHSSes) via a novel backstepping-based delayed impulsive correction control scheme, where the time delay in impulsive actions is fully considered and rigorously proven to facilitate system stabilization. First, a third-order nonlinear model of EHSS is established with explicit consideration of external disturbances. Then, a recursive backstepping method is developed to derive virtual control laws for the position velocity subsystem, rendering it ISS with respect to the acceleration error. Furthermore, by employing Lyapunov stability theory, impulsive delay inequalities, and ISS lemmas, sufficient conditions are derived to guarantee the ISS of the closed-loop error system, where the stabilizing contribution of delays involved in impulses is quantitatively analyzed within the established sufficient criteria. Finally, numerical simulations are conducted to validate that the proposed control strategy.