Networked-based H∞ control for discrete-time slow sampling singularly perturbed systems via an improved event-triggered approach

This paper investigates the H-infinity control problem for a class of slow sampling singularly perturbed systems (S(3)PSs) with an improved event-triggered method (ETM). Compared with the conventional static ETM, an improved one with time-varying threshold is exploited to enhance the dynamic performance for the S(3)PSs with certain communication frequency reduction. By adjusting the threshold with the triggering error, a faster converge speed can be achieved. Sufficient conditions are derived by constructing a singular perturbation parameter (SPP) dependent Lyapunov function, with which both asymptotic stability can be guaranteed for the closed-loop S(3)PSs and the ill-conditioned numerical issues can be avoided. By resorting to the matrix inequality techniques, an ETM-based controller can be developed within the upper bound of the SPP. Further demonstration for the feasibility of the proposed algorithm is presented by designing an ETM-based controller for an inverted pendulum system.