Finite-Time Stabilization of Uncertain Delayed T–S Fuzzy Systems via Intermittent Control
Rongqiang Tang, Xinsong Yang, Peng Shi, Zhengrong Xiang, Linbo Qing
Abstract
This article focuses on finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math></inline-formula> stabilization of T–S fuzzy systems with time delays and parameter uncertainties via intermittent control. To cope with the effects of parameters uncertainties, time delays, and intermittent divergence simultaneously, a new finite-time stability lemma for intermittently controlled systems is presented. Then, a weighted 2-norm Lyapunov–Krasovskii functional (LKF) is established, which has the advantage that it is convenient to derive less conservative linear matrix inequality sufficient conditions and to overcome the difficulty in analyzing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math></inline-formula> performance under intermittent control frameworks. Another advantage of our result over existing results is that the growth increment of the LKF on the noncontrolled interval can be larger than the decreasing magnitude on the controlled interval. The merits of the theoretical results are examined by a numerical example and a coupled Chua's circuit.