On designing of sliding-mode control for stochastic jump systems
On designing of sliding-mode control for stochastic jump systems
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DOI：
10.1109/tac.2005.861716
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发表时间：
2006-01
影响因子：
6.8
通讯作者：
P. Shi;Yuanqing Xia;Guoping Liu;D. Rees
中科院分区：
文献类型：
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作者：
P. Shi;Yuanqing Xia;Guoping Liu;D. Rees
本文研究了一类具有随机跳变的线性连续时间系统的随机稳定性和滑模控制问题，其中跳变参数被建模为连续时间、离散状态的齐次Markov过程，其右连续轨迹取值于有限集中.利用线性矩阵不等式方法，给出了保证系统随机稳定的充分条件。然后，到达运动控制器的设计，使得所得到的闭环系统可以被驱动到所需的滑动表面在有限的时间。证明了马尔可夫跳变系统的滑模控制问题是可解的，只要一组耦合的线性矩阵不等式有解。最后给出了一个数值例子来说明所提出的方法的潜力。
In this note, we consider the problems of stochastic stability and sliding-mode control for a class of linear continuous-time systems with stochastic jumps, in which the jumping parameters are modeled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. By using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system. Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled LMIs have solutions. A numerical example is given to show the potential of the proposed techniques.