Title :
A New Approach to
Filter Design for Systems With Time-Varying State Delay
Author :
Xiaoguang Dong ; Jianbin Qiu ; You Ma ; Huijun Gao
Author_Institution :
Res. Inst. of Intell. Control & Syst., Harbin Inst. of Technol., Harbin, China
Abstract :
This brief revisits the robust H∞ filter design problem for systems with a time-varying state delay by an indirect approach. By employing a two-term approximation method, the filtering error system with a time-varying delay is reformulated into a feedback interconnection form, which contains a forward system with two constant time delays and a feedback system with uncertainties. Then, based on the scaled small gain theorem, the asymptotic stability of the filtering error system is examined, and a new delay-dependent bounded real lemma (BRL) is obtained. Based on the BRL, both the full- and reduced-order filter design approaches are proposed. Moreover, immediate extensions of the results are made to systems with polytopic uncertainties. Finally, two illustrative examples are presented to demonstrate the validity of the proposed methods.
Keywords :
H∞ filters; approximation theory; delays; feedback; reduced order systems; time-varying systems; BRL; delay-dependent bounded real lemma; feedback interconnection form; filtering error system; forward system; full-order filter design approaches; indirect approach; polytopic uncertainties; reduced-order filter design approaches; robust H∞ filter design problem; scaled small gain theorem; time-varying state delay; two-term approximation method; Delay; Delay effects; Linear systems; Robustness; Stability analysis; Time varying systems; Uncertainty; $H_{infty}$ filtering; model reformulation; polytopic uncertainties; scaled small gain (SSG) theorem; time-varying delay;
Journal_Title :
Circuits and Systems II: Express Briefs, IEEE Transactions on
DOI :
10.1109/TCSII.2012.2218491