不确定时滞系统鲁棒镇定的优化方法

Optimization Approach to Robust Stabilization of Linear Systems with Time-delay Uncertainties

对一类含有时滞不确定的线性系统,考虑了鲁棒镇定问题。系统中的不确定性假设满足范数有界备件,通过用改进的Razmikhin-type定理,给出了鲁棒镇定控制器存在的充分条件。通过对Lyapunov矩阵方程的完全参数化求解,得到了鲁棒镇定控制器的参数化形式,鲁棒镇定问题转化为一类优化问题。基于这一条件与参数化特征结构配置结果,得到了状态反馈镇定控制器的设计算法。数值例子说明了该方法的有效性。

The robust stabilization for a class of linear systems subject to delayed and time-varying nonlinear uncertainties is presented. The structure of the uncertainties is assumed to satisfy a boundedness condition. By using an improved Razumikhin-type theorem, a sufficient condition for the existence of controllers is proposed. Based on this condition and a parametric eigenstructure assignment result, an algorithm for robust state feedback controller synthesis is presented. A numerical example demonstrates the effect of the proposed design approach.