具有不确定参数控制系统的鲁棒绝对稳定性

Robust absolute stability of control systems with uncertain parameters

利用李亚普诺夫稳定性方法和线性矩阵不等式,通过构造适当的李亚普诺夫函数,对具有结构参数扰动和范数扰动的不确定参数滞后型Lurie控制系统进行了研究,得到了该系统鲁棒绝对稳定的时滞无关充分条件;利用同样的方法,得到了该系统鲁棒绝对稳定的时滞相关充分条件.研究结果表明:这些条件是在参数不确定且参数无范数界情况下,用对角矩阵和线性矩阵的正定性表示,具有直观性和便于计算机运算等特点,并可以很方便地运用Matlab工具箱求解.

By using Lyapunov stability method, linear matrix inequalities, and the establishment proper Lyapunov function, this paper studied uncertain parameter time-delay Lurie control systems with structured parameter perturbations and norm bound parameter perturbations, and thus obtains delay-independent and delay-dependent sufficient conditions for robust absolute stability of the systems. The research shows： when parameter is uncertain and has no norm bound restriction, these above conditions can be presented in terms of the positive definite characteristic of diagonal matrix and linear matrix, which is very directly perceived and easy to operate and can be easily solved by Matlab Toolbox.