离散时间线性参数变化系统稳定性分析

Stability Analysis of Discrete-Time Linear Parameter-Varying Systems

考虑离散时间时变线性系统稳定性,其时变的系统矩阵在一个由已知顶点矩阵所构成的多胞体中。通过应用参数依赖Lyapunov函数(涉及参数增量上界),给出一个由线性矩阵不等式(LMI)表述的判据,以判别系统的鲁棒稳定性,用到参数依赖Lyapunov函数及参数增量上界。与二次稳定性及定常参数依赖的Lyapunov函数方法相比较,所得结果不仅把保守性降到一个更低水平,而且作为推论导出文献已有结果。对算例所做的比较计算证实了新方法的优越性。

The stability of time-varying discrete-time linear systems with the time-varying system matrices in a polytope domain that is a convex combination of finite vertex matrices was considered. The paper presents a criterion written in linear matrix inequalities （LMIs） to test the robust stability of the system by using a parameter-dependent Lyapunov function that deals with bounds of parameter increments. Compared with the quadratic stability and the constant-parameter-dependent Lyapunov function approaches, our result not only reduces the conservation to a lower level, but also leads to prior results as our corollaries. At last, an example calculated as compared with known approaches shows the advantage of the new approach.