Stability analysis of fuzzy systems with a time-varying delay. (Chinese. English summary) Zbl 1240.93265
Summary: A new method for the delay-dependent stability analysis for continuous-time Takagi-Sugeno (T-S) fuzzy systems with a time-varying delay is suggested, which is less conservative than other existing ones. Based on a Fuzzy Lyapunov-Krasovskii Functional (FLKF), a delay-dependent stability criterion is derived for the fuzzy systems. In the derivation process, some free-weighting matrices are introduced to express the relationships among the terms of the system equations, and among the terms in the Leibniz-Newton formula, which may avoid the conservation produced by some bounding inequalities for cross products between two vectors and model transformation. Finally, a simulation example shows that the approach is effective.
MSC:
93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
93C42 | Fuzzy control/observation systems |