Necessary and sufficient condition for the existence of a common quadratic lyapunov function for switched linear interval systems

机译：切换线性区间系统存在一个公共二次lyapunov函数的充要条件

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In this paper, a necessary and sufficient condition for the existence of a common quadratic Lyapunov function (CQLF) for continuous time n-th order switched linear interval systems (SLISs) under arbitrary switching is presented. SLISs have infinitely many subsystems that are within the specified interval. All the subsystems of SLISs can be represented as a polytope of vertices of the interval matrix. It will be shown that the existence of a CQLF for SLISs is equivalent to the existence of a CQLF for all the vertices of the systems.

机译：本文提出了在任意切换条件下连续时间n阶切换线性区间系统（SLISs）存在公共二次Lyapunov函数（CQLF）的充要条件。 SLIS具有在指定间隔内的无限多个子系统。 SLIS的所有子系统都可以表示为间隔矩阵的顶点的多面体。将会显示，对于SLIS，CQLF的存在等同于系统所有顶点的CQLF的存在。

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《2011 11th International Conference on Control, Automation and Systems》|2011年|p.97-102|共6页
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Kim Byeong-Yeon; Ahn Hyo-Sung;
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中图分类自动化技术及设备;
关键词
Common quadratic Lyapunov function; Polytope of matrices; Switched linear interval systems; Vertex matrix;

机译：常见二次Lyapunov函数;矩阵的多边形;切换线性区间系统;顶点矩阵;

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1. 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
2. Existence of a common quadratic lyapunov function for discrete switched linear systems with m stable subsystems [J] . Sun C., Fang B., Huang W. Control Theory & Applications, IET . 2011,第3期

机译：具有m个稳定子系统的离散线性切换系统的通用二次lyapunov函数的存在性
3. A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation [J] . M.A. Duarte-Mermoud, R.H. Ordonez-Hurtado, P. Zagalak International journal of systems science . 2012,第10a12期

机译：基于粒子群算法的切换线性系统公共二次Lyapunov函数不存在的确定方法
4. Necessary and sufficient condition for the existence of a common quadratic lyapunov function for switched linear interval systems [C] . Kim Byeong-Yeon, Ahn Hyo-Sung International Conference on Control Automation and Systems . 2011

机译：用于切换线性间隔系统的常见二次Lyapunov函数的必要和充分条件
5. Necessary and sufficient conditions for global asymptotic stability of third-order conewise linear systems [D] . Shokralla, Shaddy Samir Zaki 2006

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6. Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems [O] . Ioan-Lucian Popa, Mihail Megan, Traian Ceauşu 2013

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7. A Geometrical Treatment for Obtaining Necessary and Sufficient\ud Conditions for Joint Quadratic Lyapunov Function Existence for\ud State-Dependent, Switched Systems: A Two-Dimensional Case [O] . Griggs, Wynita M., King, Christopher K., Shorten, Robert N., 2009

机译：获得必要和充分\ ud的几何处理 \ ud的联合二次Lyapunov函数存在的条件状态相关的交换系统：二维情况

Necessary and sufficient condition for the existence of a common quadratic lyapunov function for switched linear interval systems

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