Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems

• Autorzy: Duan R. , Li J. , Zhang Y. , Yang Y. , Chen G.

Identyfikatory

DOI

10.1515/amcs-2016-0009

• Języki publikacji: EN

Abstrakty

EN

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H_∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.

Słowa kluczowe

EN

discrete T–S fuzzy hyperbolic model; parallel distributed compensation; positive diagonally dominant matrices; robust stability

PL

model Takagi-Sugeno; kompensacja rozproszona; sterowanie odporne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2016
• Tom: Vol. 26, no. 1
• Strony: 133--145
• Opis fizyczny: Bibliogr. 48 poz., wykr.

Twórcy

autor

Duan R.

• School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

autor

Li J.

• School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

autor

Zhang Y.

• School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

autor

Yang Y.

• Department of Mathematics, Huizhou University, Huizhou, Guangdong Province, 516007, China

autor

Chen G.

• Department of Mathematics, Huizhou University, Huizhou, Guangdong Province, 516007, China

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.