Decentralized piecewise H∞ fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay. Issue 9 (September 2015)

• Record Type: Journal Article
• Authors: Zhong, Zhixiong; Fu, Shasha; Hayat, Tasawar; Alsaadi, Fuad; Sun, Guanghui
• Is Part Of: Journal of the Franklin Institute. Volume 352:Issue 9(2015:Sep.)
• Page Start: 3782
• Page End: 3807
• Publication Date: 2015-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2015.01.033
• Languages: English
• ISSNs: 0016-0032

Abstract

<abstract abstract-type="author" id="ab0005"> <title id="sect0005">Abstract</title> <sec> <p id="sp0060">This paper investigates the problem of decentralized piecewise <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0005.gif" overflow="scroll" id="d13e551" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> filtering design for a class of discrete-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of a number of nonlinear subsystems, and each nonlinear subsystem is represented by a Takagi–Sugeno (T–S) model. The time-varying state delay of each subsystem is assumed to be of an interval-like type with lower and upper bounds. The objective is to design a decentralized piecewise filter such that the filtering error system is asymptotically stable with a guaranteed <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0005.gif" overflow="scroll" id="d13e560" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0005.gif" overflow="scroll" id="d13e569" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> filtering problem is reformulated in the context of input–output (IO) stability. Based on a piecewise Lyapunov–Krasovskii functional (PLKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized piecewise <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0005.gif" overflow="scroll" id="d13e578" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> filtering design of the large-scale T–S fuzzy system in terms of linear matrix inequalities. Two examples are provided to illustrate the effectiveness of the proposed method.</p> </sec> </abstract>