不确定离散时滞系统的时滞相关保性能控制

Delay-dependent Guaranteed Cost Control of Uncertain Discrete Time-delay Systems

针对一类范数有界不确定离散状态时滞系统,研究了系统时滞相关保性能控制问题.通过在李亚普诺夫函数的前向差分中引入零项式和松弛变量,得到了改进的系统保性能控制律存在的时滞相关条件.针对控制律存在的时滞相关条件不是用严格线性矩阵不等式表示的情况,得到了一个改进的求解非凸可行性问题的迭代算法.通过两个数值例子表明所得结论能得到更小的性能指标上界.

The problem of guaranteed cost control for discrete time-delay systems with norm-bounded uncertainties is considered.An improved delay-dependent condition for the existence of the guaranteed cost controller is developed by introducing a zero formula and slack variable in the forward difference of Lyapunov functional.As the condition is not expressed using strict linear matrix inequlity（LMI） conditions,an iterative algorithm is proposed to solve the non-convex feasibility problem.Two numerical examples show that the proposed method can even give a smaller upper bound for the performance index.