具有饱和执行器的不确定离散时滞系统的镇定

摘要

Dynamic characteristics of the actuator will often introduce some non-linear characteristics,the common one is saturation.This paper discusses the robust stabilization problem of discrete time-delay uncertain system with actuator saturation.First of all,since the nonlinear characteristics of saturated actuator will have great influence on the stability of the system,the paper deals with saturated nonlinear item by using fan zone method.Secondly,using Lyapunov function method,combined with matrix inequality properties,the paper proposes an existence condition of memory-less state feedback controller,and under the stability conditions of the closed-loop system,the nonlinear matrix inequality was transformed into linear matrix inequality.The sufficient condition not only eliminates the influence of uncertainties on the stability of the system,but also reaches the time-delay independent stability criterion.Finally,a numerical example illustrates the feasibility and effectiveness of the results.%执行器的动态特征常常会引入某些非线性特性，其中常见的就是饱和。针对控制系统中广泛存在的饱和问题，讨论了具有饱和执行器的离散常时滞不确定系统的鲁棒镇定问题。首先，由于饱和执行器的非线性特性会对系统的稳定性有较大影响，所以利用扇形区域法对饱和非线性项进行处理。其次，利用李雅普诺夫函数方法，结合矩阵不等式性质，给出了无记忆状态反馈控制律存在的充分条件，并且在闭环系统渐近稳定的条件下，将所得的非线性矩阵不等式转化成线性矩阵不等式，该充分条件不仅消除了不确定项对系统稳定性的影响，而且得到了与时滞无关的稳定性判据。最后，给出一个数值仿真算例，验证了所得结果的有效性和可行性。