Reducing conservativeness in recent stability conditions of TS fuzzy systems

Fuzzy control turns 50: 10 years later

“…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].…”

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

“…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].…”

Robust Stabilization for Uncertain Takagi-Sugeno Fuzzy Continuous Model with Time-Delay Based on Razumikhin Theorem

“…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].…”