广义转移速率条件下连续时间奇异Markov跳变系统的随机容许性分析

针对一类连续时间奇异Markov跳变系统,研究了其随机容许性的问题。首先,引入广义转移速率的概念,同时给出了该类奇异Markov跳变系统正则、无脉冲、随机稳定的充分性判据;其次,对广义转移速率进行分类处理,利用严格线性矩阵不等式和Schur补理论得出系统随机容许性的充分条件;最后,设计状态反馈控制器,确保系统满足随机容许性,并给出系统状态反馈矩阵表示形式。

不确定时滞马尔可夫切换广义系统的鲁棒严格耗散控制

首先将严格耗散概念引入到时滞马尔可夫切换广义系统中,然后利用线性矩阵不等式给出了该系统随机容许且严格耗散的充分条件;进而设计状态反馈鲁棒严格耗散控制器,使闭环系统鲁棒随机容许且严格耗散.

离散马尔可夫跳跃广义系统的鲁棒严格耗散控制

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.

离散广义Markov跳变系统在一般转移率下的鲁棒稳定性

考虑一类离散广义Markov跳变系统在一般转移率下的鲁棒稳定性问题.针对一般转移率下的离散广义Markov跳变系统,运用自由权矩阵方法,给出了离散广义Markov跳变系统随机容许的充分条件.

Variable structure control for descriptor Markovian jump systems subject to partially unknown transition probabilities

The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.