针对一类离散奇异Markov跳变系统, 在其模式跳变的部分转移概率未知的情况下, 研究了稳定性和镇定性问题. 通过引入松散变量, 得到了保证系统随机稳定的充分性判据, 并以线性矩阵不等式(linear matrix inequalities, LMIs)的形式表示, 给出了相应的状态反馈控制器设计方法. 算例验证了该研究的有效性及其保守性小的特点.
This paper discusses stability and stabilization for a class of discrete-time singular Markov jump systems with partly unknown transition probabilities. By introducing slack matrix variables, a sufficient condition is obtained to guarantee stochastic stability of open-loop systems. A method for designing state feedback controller is then proposed. These conditions are given in terms of linear matrix inequalities (LMIs). A numerical example is given to show effectiveness and less conservatism of the obtained results.
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