A Krein space-based approach to event-triggered H∞ filtering for linear discrete time-varying systems

• Published in: Automatica (Oxford) Vol. 135; p. 110001
• Main Authors: Zhong, Maiying, Ding, Steven X., Han, Qing-Long, He, Xiao, Zhou, Donghua
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2022
• Subjects: [formula omitted] filtering; Event-triggering mechanism; Krein space; Linear discrete time-varying system; Projection; Krein space; Projection; Linear discrete time-varying system; H∞ filtering; Event-triggering mechanism
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2021.110001

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.