A Krein space-based approach to event-triggered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e264" altimg="si5.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 linear discrete time-varying systems

This paper is concerned with the problem of event-triggered H ∞ filtering for linear discrete time-varying (LDTV) systems. Using the lifting technique, we firstly establish an equivalent relationship with a certain equivalent minimum problem of indefinite quadratic form subject to LDTV systems with non-uniform sampling periods. Then, based on Krein space projection and innovation analysis, sufficient and necessary conditions for the existence of desired filter are derived and a feasible solution is obtained in terms of Riccati recursions. Thus, an algorithm based on the time-update and event-update recursions is given for the implementation of event-triggered H ∞ filtering. Different from some existing results, a new event-triggered H ∞ filtering scheme is provided so that the estimation error can be completely decoupled from the event-triggered transmission error. Moreover, the new proposed Krein space approach is less conservative and more computational attractive than the existing methods based on recursive linear inequality matrix. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.