含参数不确定性的马尔可夫跳变过程鲁棒正实控制

讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状 态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依 赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含 参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.

Robust Positive Real Control of Markov Jump Systems with Parametric Uncertainties

The positive real analysis and synthesis problems are investigated for a class of linear systems with random jump parameters. The dynamics of the jump parameters is modeled by a continuous-time finite-state Markov process. Based on stochastic Lyapunov functional approach, both state and output-feedback mode-dependent controllers are proposed to guarantee the strict positive realness of the resulting closed-loop systems. For the Markov jump systems subject to parametric uncertainties, sufficient conditions which are in terms of solutions of a set of coupled linear matrix inequalities are developed to design robust controllers such that stochastic stability and positive realness property hold irrespective of all admissible uncertainties.