ABSTRACT

The pth moment stability of stochastic Markov jump systems (SMJSs) with time-delays and polynomial growth was investigated in this paper. Both the involved time-delays and polynomial growth are mode dependent. By using the new property of the polynomial as well as the relation between the time-delay and the generator of the Markov-chain, sufficient pth moment stability criteria are proposed. Meanwhile, the robustness of the stable SMJSs is also considered, which reveals that how much perturbation the stable SMJSs can tolerate. As an application, the consensus of stochastic multi-agent systems with nonlinear dynamics is investigated. Finally, the effectiveness of our results is illustrated by examples.

摘要

本文研究了具有时滞和多项式增长的随机马尔可夫跳跃系统(SMJS)的p阶矩稳定性。所涉及的时间延迟和多项式增长都依赖于模式。利用多项式的新性质以及时延与马尔可夫链生成器之间的关系，提出了充分的p阶矩稳定性判据。同时，还考虑了稳定 SMJS 的鲁棒性，这揭示了稳定 SMJS 可以容忍多少扰动。作为一个应用，研究了具有非线性动力学的随机多智能体系统的一致性。最后，通过示例说明了我们结果的有效性。