Real-world control applications often involve complex dynamics subject to abrupt changes or variations. Markov jump linear systems (MJS) provide a rich framework for modeling such dynamics. Despite an extensive history, theoretical understanding of parameter sensitivities of MJS control is somewhat lacking. Motivated by this, we investigate robustness aspects of certainty equivalent model-based optimal control for MJS with quadratic cost function. Given the uncertainty in the system matrices and in the Markov transition matrix is bounded by $\epsilon$ and $\eta$ respectively, robustness results are established for (i) the solution to coupled Riccati equations and (ii) the optimal cost, by providing explicit perturbation bounds which decay as $\mathcal{O}(\epsilon + \eta)$ and $\mathcal{O}((\epsilon + \eta)^2)$ respectively.

翻译：马尔科夫跳线系统(MJS)为模拟这种动态提供了一个丰富的框架。尽管历史悠久,但对于MJS控制的参数敏感性的理论理解还是有些缺乏。为此,我们调查了具有二次成本功能的MJS基于模型的确定性等同最佳控制模型的稳健性方面。鉴于系统矩阵和Markov过渡矩阵的不确定性,分别受美元和美元的约束,因此确定了以下两方面的稳健性结果:(一) 结合Riccati方程式的解决方案和(二) 最佳成本,为此,我们提供了以 $\mathcal{O}(\ epsilon +\eta) 美元和$\mathcal{O}((( epsilon +\eta)2美元) 的明显扰动界限。