SOS-based fuzzy stability analysis via homogeneous Lyapunov functions

Author

Ji-Chang Lo ; Yu-Tse Lin ; Wei-Sheng Chang ; Fong-Yi Lin

Author_Institution

Nat. Central Univ., Jhongli, Taiwan

fYear

2014

fDate

6-11 July 2014

Firstpage

2300

Lastpage

2305

Abstract

The class of polynomial fuzzy-model-based (PFMB) control systems has gained considerable attention in fuzzy control. The PFMB control system under consideration often assumes that the Lyapunov functions are quadratic, allowing use of semidefinite programming and the sum of squares (SOS) decomposition. This paper introduces a homogeneously polynomial Lyapunov function for a stabilization problem in which the state feedback synthesis based on SOS decomposition is proposed. To verify the analytical theories regarding PFMB stabilization with the proposed method, two examples are demonstrated to show the effectiveness of the proposed approach.

Keywords

Lyapunov methods; fuzzy control; mathematical programming; polynomials; stability; state feedback; PFMB control systems; PFMB stabilization; SOS decomposition; SOS-based fuzzy stability analysis; fuzzy control; homogeneous Lyapunov functions; homogeneously polynomial Lyapunov function; polynomial fuzzy-model-based control systems; semidefinite programming; state feedback synthesis; sum of square decomposition; Control systems; Fuzzy systems; Lyapunov methods; Numerical stability; Polynomials; Stability analysis; Vectors; Homogeneous Lyapunov function; Polynomial TS Fuzzy Models; Sum Of Squares (SOS);

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems (FUZZ-IEEE), 2014 IEEE International Conference on

Conference_Location

Beijing

Print_ISBN

978-1-4799-2073-0

Type

conf

DOI

10.1109/FUZZ-IEEE.2014.6891652

Filename

6891652