Title :
Asymptotically necessary and sufficient stability conditions in the sense of homogeneously polynomially nonquadratic Lyapunov functions for discrete-time Takagi-Sugeno systems
Author_Institution :
Coll. of Autom., Chongqing Univ., Chongqing, China
Abstract :
This paper considers stability of discrete-time nonlinear systems in Takagi-Sugeno´s form. This problem has been studied over twenty years with many sufficient conditions, and asymptotically necessary and sufficient (ANS) conditions in the sense of common quadratic Lyapunov function, having being obtained. This paper considers general forms of homogeneously polynomially nonquadratic Lyapunov (HPNQL) function and homogeneously polynomially parameterized (HPP) state feedback laws. By generalizing the procedure based on Polya´s theorem, which has been studied previously in different context, ANS stability conditions in the sense of HPNQL function are obtained.
Keywords :
Lyapunov methods; asymptotic stability; discrete time systems; nonlinear control systems; polynomials; state feedback; Polya theorem; asymptotical stability; discrete-time Takagi-Sugeno systems; discrete-time nonlinear systems; homogeneously polynomially nonquadratic Lyapunov functions; homogeneously polynomially parameterized state feedback laws; Asymptotic stability; Automation; Feedback; Fuzzy control; Lyapunov method; Nonlinear control systems; Polynomials; Sufficient conditions; Takagi-Sugeno model; Time varying systems;
Conference_Titel :
Control and Automation, 2009. ICCA 2009. IEEE International Conference on
Conference_Location :
Christchurch
Print_ISBN :
978-1-4244-4706-0
Electronic_ISBN :
978-1-4244-4707-7
DOI :
10.1109/ICCA.2009.5410281