Reducing conservativeness in recent stability conditions of TS fuzzy systems

Mozelli, Leonardo Amaral; Palhares, Reinaldo M.; Souza, Fernando O.; Mendes, Eduardo M. A. M.

doi:10.1016/j.automatica.2009.02.023

Cited by 256 publications

(118 citation statements)

References 9 publications

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“…A first family of results deals with the assumption, originally stated in [40], of bounded membership-function time derivatives, i.e., existence of known scalars φ i such that |μ i (z)| ≤ φ i . Results in this line appear in, for instance, [66]. Although the assumption is understandable for stability results, when z ≡ x, which is the case in nonlinear systems modelled as TS ones, it is more questionable for stabilization as, by chain rule, dµi(x) dt = ∂µi ∂x Tẋ andẋ can contain the to-be-designed control action in a general case, so the validity region of the obtained controller must be checked a posteriori, see discussion in [67].…”

Section: Non-quadratic Lyapunov Functionsmentioning

confidence: 85%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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Section: Non-quadratic Lyapunov Functionsmentioning

confidence: 85%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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show abstract

“…However, it is recognized that the common quadratic Lyapunov function is independent of membership functions, which may lead to conservativeness. To further reduce the conservatism in stability analysis, several non-quadratic Lyapunov functions have been proposed, such as piecewise Lyapunov functions [4,5,22] and fuzzy Lyapunov functions [1,2,8,12,15,17,18].…”

Section: Introductionmentioning

confidence: 99%

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Zhao¹,

Xiao²,

Ding³

et al. 2014

Kybernetika

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“…Two classes of Lyapunov functions are used to analysis these systems: quadratic Lyapunov functions and non-quadratic Lyapunov ones which are less conservative than first class. Many researches are investigated with non-quadratic Lyapunov functions [4]- [6], [7].…”

Section: Introductionmentioning

confidence: 99%