转移概率部分已知的Markov跳变系统鲁棒H_2控制

研究一类具有多胞型不确定性的Markov跳变连续时间系统的鲁棒H2控制问题.这类系统跳跃过程中的转移概率包括完全已知、未知但已知转移概率的上下界和完全未知三种情况.首先针对此类Markov跳变系统,基于参数依赖型Lyapunov函数给出新的鲁棒稳定性判据,然后在线性矩阵不等式的框架下得到相应的鲁棒H2控制器设计方法.数值仿真算例验证了本方法的有效性.

Robust H2 Control for Uncertain Markov Jump Linear Systems with Partly Known Transition Rates

The robust H2 control problem for a class of continuous-time Markov jump linear systems with polytopic-type parameter uncertainty was investigated. The considered transition probabilities includes completely known case, partly unknown with known lower and upper bounds case and completely unknown case. Firstly, based on the parameter-dependent Lyapunov function, new stability condition for this kind of uncertain Markov jump systems was derived. And then, the corresponding robust H2 controller design method was proposed in the framework of linear matrix inequalities. Finally, numerical examples were given to demonstrate the effectiveness of the proposed method.