This paper investigates the problem of sliding mode control (SMC) design under the finite-state Markov digital block-fading channels. Before transmitting through the independent digital channels, the output measurements are first quantized through logarithmic quantizers. Then, $p$ independent finite-state hidden Markov models are introduced to model the time-varying effects subject to error-free packet arrival rates. A new one-to-one mapping rule is proposed for reformulating $p$ Markov chains into a new Markov chain. By means of the information from the mode detectors, we construct the detected mode-dependent state observer and the corresponding sliding mode controller. Both the exponential mean-square stability of the closed-loop system and the reachability of the specified sliding surface are analyzed through the fading mode-dependent Lyapunov function method. Furthermore, by adopting the binary genetic algorithm (GA), an optimizing quasi-sliding mode is further achieved. Finally, an illustrative example is provided to verify the effectiveness of the proposed method.

本文研究了有限状态马尔可夫数字块衰落信道下的滑模控制（SMC）设计问题。在通过独立数字通道传输之前，输出测量值首先通过对数量化器进行量化。然后，$磷$引入了独立的有限状态隐马尔可夫模型来模拟受无错误数据包到达率影响的时变效应。提出了一种新的一对一映射规则来重新制定$磷$马尔可夫链转化为新的马尔可夫链。借助来自模式检测器的信息，我们构建了检测到的模式相关状态观测器和相应的滑模控制器。闭环系统的指数均方稳定性和指定滑动面的可达性都通过衰落模式相关的Lyapunov函数方法进行分析。此外，通过采用二元遗传算法（GA），进一步实现了优化的准滑动模式。最后，提供了一个说明性的例子来验证所提出方法的有效性。