Finite-Time H Filtering for T-S Fuzzy Discrete-Time Systems With Time-Varying Delay and Norm-Bounded Uncertainties

• Published in: IEEE transactions on fuzzy systems Vol. 23; no. 6; pp. 2427 - 2434
• Main Authors: Zhuo Zhang, Zexu Zhang, Hui Zhang, Peng Shi, Reza Karimi, Hamid
• Format: Journal Article
• Language: English
• Published: IEEE 01.12.2015
• Subjects: Delay effects; Delays; Educational institutions; Filtering; finite-time boundedness; H∞ filtering; Linear matrix inequalities; linear matrix inequalities (LMIs); norm-bounded uncertainties; T-S fuzzy system; time-delay; Time-varying systems; Uncertainty; T–S fuzzy system; time delay; norm-bounded uncertainties; linear matrix inequalities (LMIs); H∞ filtering; Finite-time boundedness
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2015.2394380

In this paper, we investigate the filtering problem of discrete-time Takagi-Sugeno (T-S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and H ∞ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are proposed and the filter gain matrices can be obtained by calculating a set of linear matrix inequalities. A numerical example is used to illustrate the effectiveness of the proposed approaches.