基于滑动扇区的马尔科夫跳变系统的变结构控制

Sliding Sector-Based Variable Structure Control for Markov Jump System

针对一类带有不确定性的马尔科夫跳变连续时间线性系统,给出一种基于滑动扇区方法的变结构控制策略,该控制策略能够实现闭环系统二次稳定.首先给出马尔科夫跳变系统的滑动扇区的定义,进一步给出一种基于线性矩阵不等式(LMI)技术的滑动扇区的设计方法,并通过理论证明设计的控制律能够使得马尔科夫跳变不确定系统二次稳定.数值仿真算例验证了控制方案的有效性.

For a class of continuous-time Markov jump linear uncertain systems, a variable structure control strategy was design to achieve quadratic stability based on sliding sector methods. The definition of the sliding sector for Markov jump system was firstly presented, and then based on linear matrix inequality technique, the design method of the sliding sector for Markov jump linear system was given. Finally, the variable structure control strategy for Markov jump linear system was developed. It was proved that quadratic stability is obtained by using the proposed method, and result of a numerical simulation example indicated the efficiency of the developed stability.