Exact solutions to fuzzy PD-LMIs via SOS

Author

Lo, Ji-Chang ; Liu, Ming-Zhe

Author_Institution

Fac. of the Mech. Eng., Nat. Central Univ., Jhongli, Taiwan

fYear

2010

fDate

18-23 July 2010

Firstpage

1

Lastpage

6

Abstract

Based on recent results on Sum of Squares (SOS) to polynomial theory, we address exact relaxation to quadratic stability arisen from stability analysis and controller synthesis in the fuzzy control systems represented by TS models. In this paper, we show how to characterize the exact solution to the quadratic stability and by approximating the cone of copositive matrices via SOS that is solvable by SOSTOOLS. Certificate of convergence of such copositive relaxation is provided. Examples from current results are provided to illustrate our approach. It is shown that SOS relaxations can characterize exactness of the decision problems.

Keywords

approximation theory; asymptotic stability; control system synthesis; fuzzy control; linear matrix inequalities; polynomials; SOSTOOLS; controller synthesis; copositive matrice; exact relaxation; fuzzy PD-LMI; fuzzy control system; linear matrix inequality; polynomial theory; quadratic stability; stability analysis; sum of square; Asymptotic stability; Fuzzy control; Linear matrix inequalities; Polynomials; Stability analysis; Symmetric matrices; Exact solutions; Linear matrix inequality (LMI); Sum of Squares (SOS); TS fuzzy models;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems (FUZZ), 2010 IEEE International Conference on

Conference_Location

Barcelona

ISSN

1098-7584

Print_ISBN

978-1-4244-6919-2

Type

conf

DOI

10.1109/FUZZY.2010.5584563

Filename

5584563