Title :
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
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);
Conference_Titel :
Fuzzy Systems (FUZZ-IEEE), 2014 IEEE International Conference on
Conference_Location :
Beijing
Print_ISBN :
978-1-4799-2073-0
DOI :
10.1109/FUZZ-IEEE.2014.6891652
