Krein space-based approach to dynamic event-triggered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e411" altimg="si9.svg"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> filtering for a class of nonlinear discrete time systems

This paper investigates the problem of H ∞ 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 ∞ filtering performance degradation caused by an event-triggering mechanism. Moreover, the design of the event-triggered H ∞ filter and event-triggering mechanism can be carried out independently. Second, the event-triggered H ∞ 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 ∞ filter. Based on the first-order Taylor approximation, sufficient and necessary conditions for the existence of a dynamic event-triggered H ∞ filter are derived by employing Krein space projection, and a feasible solution is given in terms of Riccati recursions for guaranteeing the prescribed H ∞ performance. Third, an algorithm with time-update and event-update recursions is also provided to perform the dynamic event-triggered H ∞ 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.