Title :
A new fuzzy lyapunov function approach to stability analysis and control synthesis for Takagi-Sugeno fuzzy systems
Author :
Guojun Liu ; Xiang Liu ; Yangzheng Zeng
Author_Institution :
Sch. of Phys. & Electron. Technol., Hubei Univ., Wuhan, China
Abstract :
This paper addresses the problem of the stability analysis and control synthesis for continuous-time TakagiSugeno (TS) fuzzy systems. By employing the descriptor system approach and the parallel distributed compensation control scheme, sufficient stability conditions of fuzzy systems are derived based on a novel fuzzy Lyapunov function. Unlike conventional approach using a fuzzy blending of multiple quadratic Lyapunov functions, the bound of the time-derivatives of membership functions is not required in the proposed methods. In addition, the proposed methods overcome the difficulty using the fuzzy Lyapunov functions usually lead to solver the bilinear matrix inequalities. New sufficient conditions for TS fuzzy models allow a straightforward formulation in terms of linear matrix inequalities (LMIs), which can be easily solved by convex optimization techniques. Finally, a numerical example is given to the effectiveness of proposed methods.
Keywords :
Lyapunov matrix equations; compensation; continuous time systems; control system synthesis; convex programming; fuzzy control; linear matrix inequalities; stability; LMI; TS fuzzy model; bilinear matrix inequality; continuous time Takagi-Sugeno fuzzy system; control system synthesis; convex optimization technique; descriptor system approach; fuzzy Lyapunov function approach; fuzzy blending; fuzzy control system; linear matrix inequality; multiquadratic Lyapunov function; parallel distributed compensation control scheme; stability analysis; sufficient stability condition; Fuzzy control; Linear matrix inequalities; Lyapunov methods; Numerical models; Stability analysis; Vectors; Descriptor System; Fuzzy Lyapunov Function; Linear Matrix Inequalities (LMIs); Takagi-Sugeno (TS) Fuzzy Systems;
Conference_Titel :
Control and Decision Conference (CCDC), 2013 25th Chinese
Conference_Location :
Guiyang
Print_ISBN :
978-1-4673-5533-9
DOI :
10.1109/CCDC.2013.6561472