Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

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

“…Based on the result given in [20], more relaxed result has been derived by rearranging the expression of some key terms in the problem formulation [21]. More recently, by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions, some redundant terms have been removed from the problem formulation and thus less conservative stability conditions have been obtained in [22].…”

“…Recently, less conservative stability criteria for continuous-time T-S fuzzy systems have been proposed by exploring the properties of the time derivatives of normalized fuzzy weighting functions, see [19]- [21] and the literature therein.…”

Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach

“…Unlike the complete Lyapunov functional method in [7,10] and the delay partitioning technique in [11,32], in this paper a Lyapunov-Krasovskii functional containing the variable delay-partitioning tuning parameter 0 < δ < 1 is constructed, which means that different delay-partitioning tuning parameter 0 < δ < 1 can obtain different LMI-based stability condition. Our derivation towards Theorem 3.1 also adopts some newly developed integral inequalities (Lemma 2.3) in [23] while the present result is derived by some appropriate integral inequalities in Lemma 2.2.…”

“…There have been many approaches in the literature based on various mathematical tools such as (improved) Jensen inequality [1-4, 7, 15, 17, 18, 21, 24, 25, 29, 32, 32], free-weighting matrix method [13,17,29], reciprocally convex approach [16,[31][32][33] and fuzzy-weightingdependent Lyapunov function method [7,28,31,34]. Recently, a delay partitioning approach has been proposed to further reduce their conservatism, see [1,2,7,11,14,18,20,31,32,34] and references therein. Yang et al [31] proposed an improved delay partitioning approach to stability analysis of delayed T-S fuzzy systems.…”

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

“…Results of , as well as , overcome the aforementioned deficiency by providing local asymptotic conditions at the price of computationally demanding LMIs. In this paper, the FLF is used based on the work by Faria et al (2012).…”