Dynamic Event-Triggered State Estimation for Discrete-Time Singularly Perturbed Systems With Distributed Time-Delays

This paper is concerned with the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays. During the data transmission through a network channel of limited bandwidth, for the sake of collision avoidance and energy saving, a dynamic event-triggered scheme is employed to schedule the data communication from the sensors to the designed estimator. First, for a given singular perturbation parameter (SPP), by constructing a novel Lyapunov–Krasovskii SPP-dependent functional, sufficient conditions are obtained to guarantee the exponentially mean-square ultimate boundedness of the error dynamics of the state estimation. Furthermore, in the case that the SPP does not exceed a predefined upper bound, a design algorithm is developed for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded. In this case, by solving certain matrix inequalities, the estimator gain is characterized without needing to know the exact SPP (as long as it stays below the given upper bound). Moreover, the ultimate bound of the error dynamics is estimated. Finally, simulation results are given to confirm the validity and advantages of the proposed design scheme of the state estimator.