This paper is concerned with the problem of self-triggered multi-mode control for a class of Markovian jump systems, in which the system states are transmitted to the controller via a communication network with limited bandwidth. In order to achieve the desired performance of the closed-loop system via utilizing a controller with fewer modes, a mode monitoring mechanism related to the system modes is employed to describe the jumping characteristics among different controller modes. Based on the mode monitoring mechanism, a multi-mode controller is constructed, in which the number of controller modes may be fewer than the one of system modes. Moreover, a self-triggered strategy is developed to reduce network loads, according to which the next triggering instant on state transmission is calculated via the past and current transmitted states at the triggering instants. By introducing a sufficiently small scalar, a solving algorithm is proposed for obtaining the self-triggered multi-mode controller gains to ensure the stochastic stability of the closed-loop system with the given ${\mathcal{L}}_2$ gain performance. Finally, the simulation results are provided to illustrate the proposed self-triggered control scheme.

本文研究一类马尔可夫跳跃系统的自触发多模式控制问题，其中系统状态通过带宽有限的通信网络传输到控制器。为了通过使用模式较少的控制器来实现闭环系统的预期性能，采用与系统模式相关的模式监控机制来描述不同控制器模式之间的跳跃特性。基于模式监控机制，构建多模式控制器，其中控制器模式的数量可能少于系统模式的数量。此外，还开发了一种自触发策略来减少网络负载，根据它，状态传输的下一个触发时刻是通过触发时刻的过去和当前传输状态计算的。通过引入足够小的标量，提出了一种求解算法来获得自触发多模式控制器增益，以确保给定闭环系统的随机稳定性${\mathcal{大号}}_{\mathrm{2个}}$获得性能。最后，提供了仿真结果来说明所提出的自触发控制方案。