一类不确定离散切换广义系统的一致有限时间稳定准则

Uniform finite-time stability for a class of uncertain discrete-time switched singular systems

利用Lyapunov-like函数方法和线性矩阵不等式(linear matrix inequality,LMI)技术研究了一类不确定离散时间切换广义系统的一致有限时间稳定和状态反馈镇定问题。首先,在任意给定的切换规则且假定不确定参数项范数有界的情况下,给出了保证不确定离散切换广义系统一致有限时间有界和有限时间稳定的充分条件和状态反馈控制器的设计方法,然后利用Matlab中的LMI工具箱对建立的LMI问题进行求解。最后的仿真算例验证了所提方法的有效性。

The uniform finite time stability and feedback stabilization for a class of uncertain discrete-time switched singular systems are studied based on the Lyapunov like function approach and the linear matrix ine- quality （LMI）. Firstly, supposing that the uncertain parameters are norm bounded, a new sufficient condition which ensures uniform finite time stabliling and finite-time bounded for the uncertain discrete-time switched sin- gular systems and state feedback controller is given with arbitrary switching signals. Then, an LMI problem is formulated and solved by the LMI toolbox in Matlab. Finally, an illustrative example shows the effectiveness of the proposed method.