New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays
研究了具有连续时变时滞分量的马尔可夫跳变广义神经网络的渐近稳定性，通过构造新型Lyapunov-Krasovskii泛函和积分不等式技术，以线性矩阵不等式形式给出了时滞依赖的稳定性条件，并用五个数值例子验证了方法的有效性。
This paper examines the problem of asymptotic stability criteria for Markovian jump generalized neural networks with successive time-varying delay components. Generalized neural networks consist of a finite number of modes, which may jump from one mode to another according to a Markovian chain with known transition probability. By constructing novel augmented Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more and more information on the state vectors of the NNs, the upper bound of the successive time-varying delays is formulated. By employing a new integral inequality technique, free-weighting matrix-based integral inequality approach, and Wirtinger double integral inequality technique and that is combined with the reciprocally convex combination approach to estimate the single and double integral terms in the time derivative of the LKFs, a new set of delay-dependent conditions for the asymptotic stability of the considered NNs are represented in the form of linear matrix inequalities. Finally, five numerical examples are given to verify the effectiveness of the proposed approach with a four-tank benchmark real-world problem.