Lyapunov stability analysis of higher-order 2-D systems
Lyapunov stability analysis of higher-order 2-D systems
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DOI：
10.1109/cdc.2009.5399822
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发表时间：
2009-11
影响因子：
2.5
通讯作者：
C. Kojima;P. Rapisarda;K. Takaba
中科院分区：
文献类型：
--
作者：
C. Kojima;P. Rapisarda;K. Takaba
本文证明了由高阶线性偏差分方程组描述的二维系统渐近稳定的一个充分必要条件。我们证明了渐近稳定性等价于存在一个满足一定正性条件的向量李雅普诺夫泛函以及它沿系统轨迹的沿着发散。我们使用的行为框架和微积分的二次差分形式的基础上四变量多项式代数。
In this paper we prove a necessary and sufficient condition for the asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra.