具有随机延时的网络控制系统的均方可镇定性分析

Mean-square stabilizability of networked control system with random communication delays

针对网络系统的可镇定性问题,研究整数步随机延时离散时间线性系统的均方可镇定性.利用Youla参数化与内外分解方法,结合均方小增益定理得到系统输出反馈均方可镇定的充分必要条件.该条件明确给出系统可镇定性与被控对象特性(不稳定极点、非最小相位零点、相对阶)和信道特性(频域信噪比函数)的关系,其中频域信噪比函数在被控对象不稳定极点的取值对可镇定影响甚大.利用仿真算例量化被控对象的非最小相位零点及相对阶对可镇定性的影响,验证可镇定性条件的正确性.

This paper studies the mean-square stabilizability for linear system with random integer-steps delays in discrete time.The fundamental condition of mean-square stabilizability which ensures that an open-loop unstable system can be stabilized by output feedback in the mean-square sense is obtained in terms of applying the Youla parametrization and inner-outer factorization methods to the innovative mean-square small gain theorem.This condition,both necessary and sufficient,provides a fundamental limit imposed by the plant’s characteristic(unstable poles,nonminimum phase zeros,relative degree)and the channel’s feature(frequency signal-to-noise ratio).The values of the frequency signal-to-noise ratio function at the unstable poles may aggravate the stabilizability condition.Some examples are used to quantify the effect of nonminimum-phase zeros and relative degree of the plant on stabilizability and confirm the correctness of the stabilizability condition.