New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

转移率部分未知的Markov跳变神经网络的稳定性

研究了具有Markov跳跃和区间时变时滞神经网络系统的稳定性问题。此类Markov跳变神经网络系统的转移概率矩阵元素部分未知,因而更具有一般性。通过建立新颖的增广Lyapunov泛函和应用反凸组合技术,得到了含有转移概率部分未知的Markov跳变神经网络的稳定准则。提出的方法不需要知道转移概率矩阵中未知元素的任何信息,增加了结果的使用范围。同时,得到的稳定性准则依赖于时滞的上下界。最后,通过数值仿真验证了所得结果的正确性。