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Robust stabilization of non-linear non-autonomous control systems with periodic linear approximation
IMA Journal of Mathematical Control and Information ( IF 1.5 ) Pub Date : 2020-03-16 , DOI: 10.1093/imamci/dnaa003
V I Slyn’ko 1 , Cemil Tunç 2 , V O Bivziuk 3
Affiliation  

Abstract
The paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given.


中文翻译:

具有周期线性逼近的非线性非自治控制系统的鲁棒镇定

摘要
本文讨论了稳定一族非线性非自治系统的平衡态的问题。假定标称系统是具有周期系数的线性控制系统。对于名义控制系统,提出了一种构造具有可变矩阵的二次型Lyapunov函数的新方法。该矩阵被定义为基于W.Magnus系列的部分和的分段指数函数形式的Lyapunov矩阵微分方程的近似解。构造具有分段恒定周期矩阵的线性反馈形式的稳定控制。该控制同时稳定了所考虑的系统系列。获得对所有系统都通用的闭环系统渐近稳定平衡状态的吸引域的估计。给出了一个数值例子。
更新日期:2020-03-16
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