一类转移概率部分未知的Markov跳跃系统的输入输出量化反馈控制

对一类离散时间马尔可夫跳跃系统(Markov jump systems,MJSs)的稳定性问题进行研究,考虑MJSs转移概率矩阵中的元素部分未知,且系统的控制输入通道和测量输出通道都存在信号量化的情况,其中控制器输入通道和系统输入通道的信号分别被两个不同的对数量化器量化。利用切换李雅普诺夫函数的方法,通过构造系统模态依赖且双通道量化误差依赖的李雅普诺夫函数,完成对闭环系统的稳定性分析和控制器设计。得到一组模态依赖的控制器,能够在系统的转移概率部分未知和存在双通道量化误差的条件下,保证闭环MJSs的随机稳定性。最后通过仿真实验验证了理论的有效性。

Input and output quantized feedback control for a class of Markovjump systems with partially unknown transition probabilities

The stability and stabilization problems for a class of discrete time Markov jump systems (MJSs) are concerned. A general scenario is taken into consideration: the elements of transition probability matrix are partly unknown and signal quantization exists in both control input channel and measurement output channel. The quantized signals in the above mentioned channels are quantized via two different logarithmic quantizers. By virtue of switched Lyapunov function approach, a system mode dependent and quantization error dependent Lyapunov function is constructed to solve the issues of stability analysis and controller design. A set of mode dependent controllers is designed, which is effective in tackling the quantization errors in two channels, and under the circumstance of insufficient information of transition probabilities, the resulting closed loop MJSs are stochastically stable. Finally, a numerical example is utilized to demonstrate the effectiveness of the proposed control strategy.