执行器饱和的不确定时滞系统的镇定

针对控制系统中广泛存在的饱和问题,主要讨论了具有执行器饱和的连续线性常时滞不确定系统的镇定问题。由于饱和具有典型的非线性特性,在应用李雅普诺夫稳定性理论分析饱和系统时,必须对饱和非线性项进行处理。首先,根据扇形区域法引入无记忆状态反馈处理饱和项,并假设不确定项满足范数有界性条件,应用李亚普诺夫函数方法研究系统渐近稳定的充分条件,消除了不确定部分与时滞现象对系统带来的影响。其次,在闭环系统渐近稳定的条件下,将得到的非线性矩阵不等式转化为线性矩阵不等式,给出了无记忆状态反馈控制器的存在条件和设计方案。最后,通过一个二维数值仿真算例验证了所得结果的可行性和有效性。

Stabilization of uncertain time-delay systems with actuator saturation

Aimed at the saturation which plays important roles in the control theory,the stabilization problem for continuous linear actuator saturation systems possessing norm-bounded parameter uncertainties and time-delay is considered.Due to the typical nonlinear characteristics of the saturation,the author need to deal with saturated nonlinear item when using Lyapunov stability theory in the analysis.First of all,according to the fan zone method,the author introduce the memory-less state feedback,moreover,applies the norm-bounded parameter uncertainty and Lyapunov function method to study the sufficient conditions for asymptotic stability of the system.The above methods eliminates the influence of uncertainties and time-delay.Secondly,under the stability conditions of the closed-loop system,the author propose a existence condition and design method of memory-less state feedback controller by converting the nonlinear matrix inequality to linear matrix inequality.Finally,a two-dimensional numerical simulation example illustrates the feasibility and effectiveness of the results.