随机马尔科夫跳跃系统有限时间控制

研究了转移概率部分信息未知的随机马尔科夫跳跃系统的有限时间控制问题.首先,介绍了有限时间随机稳定性与随机镇定性的概念;然后,利用矩阵变换、数学期望以及Gronwall不等式等方法,给出了系统为有限时间随机稳定的判定准则.利用上述结果,得出了系统状态输出反馈随机镇定的充分条件;进一步,考虑到实际工程中系统状态的不完全可测性,给出了保证系统有限时间随机镇定的动态输出反馈控制器设计方式,并求得了此控制器存在的判定条件.最后,用一个数值算例说明了控制器设计方法的有效性.

Finite-time control of stochastic Markovian jump systems

This paper considers the finite-time control problem for stochastic Markovian jump system subject to partial information on transition probabilities. Firstly, the concepts of finite-time stochastic stability and stabilization for stochastic Markovian jump systems are defined. Secondly, with the aid of matrix transformations, mathematical expectation and Gronwall inequality, a practical criterion, under which the stochastic systems are finite-time stochastically stable, is given. After that, a sufficient condition for stochastic stabilization via state feedback is obtained. Considering that the state of the system in practical engineering is often with partial information, we develop a dynamic output feedback controller which ensures the stochastic system to be finite-time stochastically stabilizable. The testing condition for the existence of such a controller is proved. Finally, a numerical example is given to show the validity of the designed method.