离散马尔可夫跳跃广义系统的鲁棒严格耗散控制

Robust strictly dissipative control for descriptor discrete-time Markovian jump systems

考虑具有范数有界不确定性的离散马尔可夫跳跃广义系统的严格耗散性分析和控制问题.首先将严格耗散概念引入到离散马尔可夫跳跃广义系统,利用线性矩阵不等式给出了离散马尔可夫跳跃广义系统鲁棒随机容许且严格耗散的充分条件;然后利用矩阵不等式给出了状态反馈鲁棒严格耗散控制器的存在条件和综合方法.最后通过数值算例说明了所提出方法的有效性.

The problem of strictly dissipative analysis and design is considered for descriptor discrete-time Markovian jump systems with norm-bounded uncertainty. Firstly, the conception of strict dissipativeness is introduced into descriptor discrete-time Markovian jump systems, and a sufficient condition for the uncertain discrete-time descriptor system stochastically admissible and strictly dissipative is derived by using the linear matrix inequality technique. Then the existence condition of state feedback robust strict dissipative controller is also presented for descriptor discrete-time Markovian jump systems. In addition, a method of designing state feedback robust strict dissipative controller is given. Finally, a numerical example shows the effectiveness of this method.