This paper deals with the problem of asynchronous ${\mathcal{H}}_{\infty }$ observer-based control for continuous-time nonhomogeneous Markovian jump systems with generalized incomplete transition rates. Different from other existing papers, the effects of both nonhomogeneity and asynchronism on observer-based control design are discussed in detail to address more realistic phenomena. Furthermore, to decouple the Lyapunov matrix from the control gain while improving the control performance, this paper proposes a state extension method as an alternative to the conventional separation method. Not only that, to derive a set of LMI-based stabilization conditions, this paper presents a less conservative relaxation technique that reduces its computational burden. Finally, two illustrative examples are provided to show the validity of the proposed method.

本文处理异步问题 ${\mathcal{H}}_{\infty }$具有广义不完全跃迁率的连续时间非齐次马尔可夫跳跃系统的基于观察者的控制。与其他现有论文不同，本文详细讨论了非均匀性和异步性对基于观测器的控制设计的影响，以解决更现实的现象。此外，为了在提高控制性能的同时将李雅普诺夫矩阵与控制增益解耦，本文提出了一种状态扩展方法作为传统分离方法的替代方法。不仅如此，为了导出一组基于 LMI 的稳定条件，本文提出了一种不太保守的松弛技术，以减少其计算负担。最后，提供了两个说明性例子来证明所提出方法的有效性。