LMI-based quadratic stability analysis for hierarchical fuzzy systems

Author

Park, C.-W. ; Kim, J.-H. ; Kim, S. ; Park, M.

Author_Institution

Dept. of Electr. & Electron. Eng., Yonsei Univ., South Korea

Volume

148

Issue

5

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

340

Lastpage

349

Abstract

The quadratic stability issue in a hierarchical fuzzy system is investigated and a Takagi-Sugeno (TLS) type hierarchical fuzzy controller is proposed to regulate the nth order linear SISO plant with the bounded time-varying uncertainties or nonlinearities. The proposed T-S type hierarchical fuzzy controller is made up of n-1 2D T-S type fuzzy controllers and allows for the simple closed dynamics in the diagonal norm-bound linear differential inclusions (DNLDI) formulation. For this closed dynamics, the stability condition in linear matrix inequalities (LMI) form is presented. Then, based on the stability condition, a method for finding the maximum stable ranges of the T-S type hierarchical fuzzy controller gains is proposed. To illustrate the performance of the proposed method, a third order simple example is given

Keywords

control nonlinearities; control system analysis; fuzzy control; hierarchical systems; matrix algebra; multidimensional systems; stability; time-varying systems; uncertain systems; 2D fuzzy controllers; DNLDI; LMI; LMI-based quadratic stability analysis; T-S type hierarchical fuzzy controller; Takagi-Sugeno type hierarchical fuzzy controller; bounded time-varying nonlinearities; bounded time-varying uncertainties; diagonal norm-bound linear differential inclusions; hierarchical fuzzy systems; linear SISO plant; linear matrix inequalities; maximum stable ranges; simple closed dynamics; stability condition;

fLanguage

English

Journal_Title

Control Theory and Applications, IEE Proceedings -

Publisher

iet

ISSN

1350-2379

Type

jour

DOI

10.1049/ip-cta:20010679

Filename

964305