On mode-dependent H∞ filtering for network-based discrete-time systems

• Published in: Signal processing Vol. 93; no. 4; pp. 634 - 640
• Main Authors: Li, Lin, Li, Fei, Zhang, Zexu, Xu, Jingcheng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2013; Elsevier
• Subjects: [formula omitted] Filtering; Applied sciences; Detection, estimation, filtering, equalization, prediction; Discrete-time systems; Exact sciences and technology; Information, signal and communications theory; Linear matrix inequalities (LMIs); Markov chain; Signal and communications theory; Signal, noise; Telecommunications and information theory; Transition probability uncertainty; Discrete-time systems; Markov chain; H∞ Filtering; Linear matrix inequalities (LMIs); Transition probability uncertainty; Performance evaluation; H infinite optimization; Filtering; Discrete time systems; Non linear filter; H infinite control; H; Scheduling; Mode filter; Transition matrix; Sufficient condition; Linear filter; Linear matrix inequality; Transition probability; Signal processing; Matrix method; Delay time; Reduced order model
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2012.08.018

This paper is devoted to the H∞ filtering problem for network-based discrete-time systems subject to network communication constraints. The objective is to design a network-based full-order or reduced-order filter, such that the resulting filtering error system is mean-square stable, while a prescribed H∞ disturbance attenuation levels is satisfied. A Markov chain is used to describe the network-induced delays. Then, a mode-dependent linear filter is considered, whose parameters are scheduled by the network-induced delays. By converting the partially unknown transition probability matrix to be a known convex description, and using the slack matrix approach, a new less conservative mode-dependent sufficient condition for the existence of the desired filter is derived to guarantee that the filtering error system is stochastically stable while satisfying a given H∞ performance. Based on this condition, the filter design method is proposed, and by solving some convex linear matrix inequalities, the explicit of the desired filer gain matrices is also given. Finally, a practical example is included to illustrate the effectiveness of the proposed method. ► We investigate the filtering problem for network-based systems. ► The network-induced delays are modeled via the Markov chain with partially known transition probabilities. ► The derived results are less conservative than the published ones.