具有外部扰动的离散广义系统有限时间控制

Finite-time Control of the Discrete-time Singular Systems Subject to Exogenous Disturbances

讨论一类具有有限能量的外部扰动的线性离散广义系统的有限时间控制问题。分析问题可解性,得到该问题可解的充分条件,通过状态反馈控制器和输出反馈控制器的设计,给出实现闭环系统有限时间有界的充分条件,这些充分条件可以转化为线性矩阵不等式(LMI)的可行解问题,可借助Matlab中的LMI工具箱求解,最后通过数值算例验证该方法的有效性。

The finite-time control problem for a class of discrete-time linear singular systems subject to norm-bounded exogenous disturbances is discussed. Firstly we analysis the problems of feasible solution and obtain the sufficient conditions that guarantee the problems discussed to be feasible solved. Secondly, the state feedback controller and output feedback controller are designed respectively. After that we can obtain the sufficient conditions to guarantee the closed-loop systems to be bounded in finite--time, which can be reduced to feasibility problems involving linear matrix inequalities （LMIs）. Linear matrix inequalities（LMI） in Matlab toolbox can be applied to get the solution. Finally, a numerical example is given to illus- trate the validity of this proposed method.