Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions

Graziano Chesi

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Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions

机译：时不变的不确定系统：通过齐次参数相关的二次Lyapunov函数实现稳定性和不稳定性的充要条件

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This paper investigates linear systems with polynomial dependence on time-invariant uncertainties constrained in the simplex via homogeneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). It is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem. Moreover, this condition is also necessary by using a sufficiently large degree of the HPD-QLF.

机译：本文研究了通过均质参数相关的二次Lyapunov函数（HPD-QLF）约束单纯形约束的时不变不确定性的多项式线性系统。结果表明，通过解决广义特征值问题，可以获得确定系统是稳定还是不稳定的充分条件。此外，通过使用足够大的HPD-QLF，该条件也是必要的。

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《Automatica》 |2010年第2期|共4页
作者
Graziano Chesi;
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原文格式 PDF
正文语种 eng
中图分类 TP1TP2;
关键词
Uncertain system; Stability; Instability; Lyapunov function; SMR;

机译：不确定系统;稳定性;不稳定性;李雅普诺夫函数;SMR;

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专利

1. Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions [J] . Graziano Chesi Automatica . 2010,第2期

机译：时不变的不确定系统：通过齐次参数相关的二次Lyapunov函数实现稳定性和不稳定性的充要条件
2. Robust Stability/Performance Analysis for Linear Time-Invariant Polytopically Parameter-Dependent Systems Using Polynomially Parameter-Dependent Lyapunov Functions [J] . Masayuki SATO, Dimitri PEAUCELLE 計測自動制御学会論文集 . 2007,第6期

机译：使用多项式参数相关的Lyapunov函数对线性时不变多参数参数相关系统进行鲁棒的稳定性/性能分析
3. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems [J] . Robert N. Shorten, Kumpati S. Narendra International Journal of Adaptive Control and Signal Processing . 2002,第10期

机译：存在有限数量的稳定二阶线性时不变系统的公共二次Lyapunov函数的充要条件
4. Estimation of stability regions for continuous-time systems with actuator saturation via homogeneous parameter-dependent quadratic Lyapunov functions [C] . Zhong Xiang, Wang Zenggui, Guochen Pang Chinese Control Conference . 2017

机译：通过同次参数依赖性二次Lyapunov函数估计具有致动器饱和的连续时间系统的稳定性区域
5. Parameter-dependent Lyapunov functions and stability analysis of linear parameter-dependent dynamical systems. [D] . Zhang, Xiping. 2003

机译：依赖参数的Lyapunov函数和线性依赖参数的动力系统的稳定性分析。
6. Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic [O] . Guopeng Zhou, Jinhua Huang, Fengxia Tian, 2015

机译：具有SUM调节逻辑的遗传网络的Lyapunov稳定性的充要条件
7. Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions [O] . Chesi G 2010

机译：时不变不确定系统：通过齐次参数依赖二次Lyapunov函数求稳定性和不稳定性的充分必要条件
8. Instability of Nonlinear Infinite-Dimensional Feedback Systems Using Lyapunov Functionals. [R] . Steding, T., Bergen, A. 1971

机译：基于Lyapunov泛函的非线性无限反馈系统的不稳定性。

Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions

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