Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach

Author

Kruszewski, A. ; Wang, R. ; Guerra, T.M.

Author_Institution

Mech. Eng. & Comput. Sci., Univ. de Valenciennes et du Hainaut-Cambresis, Valenciennes

Volume

53

Issue

2

fYear

2008

fDate

3/1/2008 12:00:00 AM

Firstpage

606

Lastpage

611

Abstract

The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function. The classical conditions consider a one- sample variation, here, the main results are obtained considering k samples variation, i.e., Delta_k V(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.

Keywords

Lyapunov methods; discrete time systems; fuzzy control; linear matrix inequalities; nonlinear control systems; stability; uncertain systems; Takagi-Sugeno fuzzy model; linear matrix inequality; nonquadratic Lyapunov function; stabilization; uncertain nonlinear discrete time system; Automatic control; Control systems; Density functional theory; Linear matrix inequalities; Lyapunov method; Polynomials; Robustness; Stability; State-space methods; Uncertainty; Linear matrix inequality (LMI); nonlinear discrete models; nonquadratic Lyapunov function; uncertain Takagi–Sugeno fuzzy model;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2007.914278

Filename

4471845