In this paper, stochastic interval Hopfield neural networks with time-varying delays are investigated. By applying the Razumikhin-type theorem as well as inequality technique, a set of novel sufficient criteria independent of delays are given for the exponential stability of such networks. As a by-product, for the deterministic Hopfield neural networks with time-varying delays, some delay-independent criteria for their global exponential robust stability are also obtained. The proposed results improve and extend them in the earlier literature and are easier to verify. A numerical example and simulation are also given to illustrate the effectiveness of our results.
This paper is devoted to design H∞ sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and controller parameters, sufficient conditions for asymptotically stochastic stability of sliding mode dynamics are formulated in terms of linear matrix inequalities. Finally, a single-link robot arm system is simulated to demonstrate the effectiveness of the proposed method.