时滞离散系统的渐进稳定性

摘要

The problem of asymptotic stability was investigated for a class of discrete time-delay systems with a certain control constraints, by defining the upper bound of saturation function, constructing an appropriate Lyapunov functional, applying Lyapunov stable theorem of discrete systems, and combining the technique of linear matrix inequality.The sufficient conditions of generally asymptotic stability and regional asymptotic stability for closed-loop systems were obtained.A numerical example was provided to elaborate the correctness of the results.The results show that the closed-loop system is globally asymptotically stable if the upper bound of the saturation function is equal to 0.If the upper bound of the saturation function is greater than 0, the closed-loop systems is locally asymptotically stable.The numerical example illustrates the feasibility of the given saturated controller.%通过定义饱和函数的上确界,选取Lyapunov泛函,利用离散Lyapunov稳定性理论,并结合线性矩阵不等式方法,对控制输入满足一定约束条件的时滞离散系统的渐近稳定性问题进行研究,给出判断相应的闭环系统是全局渐近稳定及局部渐近稳定的充分条件,并通过数值算例对结果进行验证.结果表明:如果引入的饱和函数的上确界等于0,则闭环系统是全局渐近稳定的;如果引入的饱和函数的上确界大于0,则闭环系统是局部渐近稳定的;数值算例说明了所给饱和控制器的可行性.