This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.

本文密切关注通过滑模控制的延迟不确定半马尔可夫跳跃复值网络的稳定性问题。相关的相应转移率取决于正常数，即停留时间，不需要服从一般指数分布。结合广义Dynkin公式和Lyapunov稳定性理论以及累积分布函数的特点，提出了一些充分的准则来确定所获得的滑模动力系统的随机稳定性。此外，设计一种新颖的滑模控制器，以确保潜在闭环系统的所有状态轨迹都能在有限时间内到达合成滑模切换面，并在随后的时间内保持在该处。论文最后给出了一个简单的例子来验证所提供的控制器设计方案的优越性和可行性。