Generalised absolute stability and sum of squares
Generalised absolute stability and sum of squares
复制标题
广义绝对稳定性和平方和
DOI：
10.1016/j.automatica.2013.01.006
复制
发表时间：
2013
期刊：
影响因子：
6.4
通讯作者：
Hancock E
中科院分区：
文献类型：
--
作者：
Hancock E
本文介绍了一个用绝对稳定性理论和平方和规划分析非线性系统的一般框架。该技术分解成一个系统的多项式向量场的反馈与非线性记忆项，这是包含在一个广义的部门不等式与多项式的界限。这种分解可用于对非线性中的不确定性进行建模，或通过较简单的多项式函数来约束难以分析的项，例如时变、非多项式或高阶非线性。使用多项式和Lur 'e型李雅普诺夫函数，这概括了那些用于推导的多变量圆和波波夫标准在经典的绝对稳定性的稳定性和吸引力区域的条件。该技术扩展了绝对稳定性理论和平方和规划的适用性。该技术的实用性与说明性的例子证明。
This paper introduces a general framework for analysing nonlinear systems using absolute stability theory and sum of squares programming. The technique decomposes a vector field into a system with a polynomial vector field in feedback with a nonlinear memoryless term, which is contained in a generalised sector inequality with polynomial bounds. This decomposition can be used to model uncertainty in the nonlinearity or to bound difficult-to-analyse terms by simpler polynomial functions, such as time varying, non-polynomial or higher order nonlinearities. Conditions for stability and regions of attraction are found using polynomial and Lur’e type Lyapunov functions, which generalise those used for the derivation of the multivariable circle and Popov criteria in classical absolute stability. The technique extends both absolute stability theory and the applicability of sum of squares programming. The usefulness of the technique is demonstrated with illustrative examples.