Improvement on Non-Quadratic Stabilization of Discrete-Time Takagi¿Sugeno Fuzzy Systems: Multiple-Parameterization Approach

Reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems based on an extended approach

“…On the basis of the T-S fuzzy model, stability criteria derived by using the Lyapunov direct method are practicable but it is usually difficult to find a common matrix satisfying all matrix inequalities [9], i.e., most of previous results are derived while their Lyapunov functions' matrices are all common matrices. In order to release the conservatism, the so-called fuzzy Lyapunov functions (FLF) have been proposed and attracted much attention [10]- [13]. For the past few years, the homogenous polynomially matrix approach has been applied to deal with the problem of stability analysis of T-S fuzzy systems in [14]- [18], respectively.…”

LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

“…Research directions to reduce the conservatism include approaches searching for general classes of Lyapunov functions, such as piecewise Lyapunov functions [9,10], fuzzy Lyapunov functions (FLFs) [11][12][13][14][15][16], a class of Lyapunov functions using line-integral [17]; polynomial Lyapunov functions [18][19][20][21]; augmented FLFs [22][23][24]; methods using information on MFs' shape [25][26][27], Pólya's theorem [28][29][30][31][32][33]; and local stability approaches [34][35][36][37][38][39][40][41][42][43][44][45]. Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42]…”

Robust stabilization of T–S fuzzy discrete systems with actuator saturation via PDC and non-PDC law

“…It has been shown in Guerra et al, (2004) that the non-PDC control laws derived by the parameter-dependent Lyapunov function-based approach could obtain less conservative stability conditions. A nonlinear controller has been designed by fuzzy non-PDC approach and non-quadratic Lyapunov function in Lee et al, (2010). An approach for discrete-time T-S fuzzy systems with time-varying state delay has been proposed via non-PDC scheme in Wu et al, (2011).…”