Krein space-based approach to dynamic event-triggered H∞ filtering for a class of nonlinear discrete time systems

This paper investigates the problem of $H_{\infty }$ filtering for a class of nonlinear discrete time systems under a dynamic event-triggered scheme. First, a new general form of event-triggered filters is considered so that the filtering error system achieves full decoupling from the so-called event-triggered transmission error, which is the major concern of $H_{\infty }$ filtering performance degradation caused by an event-triggering mechanism. Moreover, the design of the event-triggered $H_{\infty }$ filter and event-triggering mechanism can be carried out independently. Second, the event-triggered $H_{\infty }$ nonlinear filtering is formulated as a problem of indefinite quadratic form minimum, and a Krein space-based approach is proposed for the design of the event-triggered $H_{\infty }$ filter. Based on the first-order Taylor approximation, sufficient and necessary conditions for the existence of a dynamic event-triggered $H_{\infty }$ filter are derived by employing Krein space projection, and a feasible solution is given in terms of Riccati recursions for guaranteeing the prescribed $H_{\infty }$ performance. Third, an algorithm with time-update and event-update recursions is also provided to perform the dynamic event-triggered $H_{\infty }$ nonlinear filtering. It is shown that the proposed Krein space-based approach is computational attractive and easy to implement. Finally, a three-tank system is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.