Asymptotically necessary and sufficient stability conditions for discrete-time Takagi–Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials

Relaxed stability and stabilisation conditions for continuous‐time Takagi–Sugeno fuzzy systems using multiple‐parameterised approach

“…To circumvent the unavailable time derivatives of MFs, the line-integral Lyapunov function [29,30] was presented, while the Lyapunov matrices had to include a special structure, and this strong restriction could also introduce some conservatism. To further reduce the conservatism, relaxed stability or stabilisation conditions for discrete-time T-S fuzzy system have been developed by applying generalised Lyapunov functions, such as the k-sample variation Lyapunov functions [31][32][33], homogenous polynomially parameter-dependent Lyapunov functions (HPPDLFs) or homogenous polynomially non-quadratic Lyapunov functions (HPNQLFs) [8,[34][35][36][37]. It has been shown that as the k-sample or the degrees of the related HPPD matrices increase, the conservatism of stability or stabilisation conditions are gradually reduced, but as a result, the computational burden will increase.…”