基于Jensen 不等式的2-D 区间时变时滞系统的稳定与控制

考虑具有区间时变时滞二维(2-D) 离散系统的时滞相关稳定性和控制问题. 选取含有时滞上下界的Lyapunov 函数, 对其差分时考虑到所有项, 结合2-DJensen 不等式, 由线性矩阵不等式给出系统新的时滞相关稳定性准则. 准则中含有更少的待定变量, 降低了数值计算负担, 并且比一些已有结果具有更小的保守性. 基于稳定性准则, 由状态反馈实现了系统的稳定控制. 最后, 通过数值算例表明了所得结果的有效性和优越性.

Stability and control of 2-D interval time-varying delay systems based on Jensen inequality

This paper concerns the problems of delay-dependent stability and control for 2-D discrete systems with interval time-varying delays. By choosing a Lyapunov functional with the upper and lower bounds of delays and considering all terms in its difference, then combining with the 2-D Jensen inequalities, a new delay-dependent stability criteria is given in terms of linear matrix inequalities(LMIs). Less decision variables are involved in the criteria, so the burden of numerical computation is reduced. And it is less conservative than some existing ones. Based on the stability criteria, state feedback is considered to realize the stability control of the system. Finally, numerical examples are given to illustrate the effectiveness and advantage of the results.