Stability analysis of 2-D systems
Stability analysis of 2-D systems
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DOI：
10.1109/tcs.1980.1084769
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发表时间：
1980-12
期刊：
影响因子：
--
通讯作者：
E. Fornasini;G. Marchesini
中科院分区：
文献类型：
--
作者：
E. Fornasini;G. Marchesini
以2-D系统的多项式稳定性判据为出发点，引入频率相关的李雅普诺夫方程。其矩阵解的傅立叶分析导致一个无限维的二次型，它提供了一个系统的全局状态的李雅普诺夫函数。傅立叶系数被明确地获得为涉及系统矩阵的级数之和。这些级数的收敛性构成了一个充分必要的稳定性条件，推广了一维系统的类似条件。
A polynomial stability criterion for 2-D systems is taken as a starting point for introducing a frequency dependent Lyapunov equation. The Fourier analysis of its matrix solution leads to an infinite dimensional quadratic form which provides a Lyapunov function for the global state of the system. The Fourier coefficients are explicitly obtained as the sum of series involving the system matrices. The convergence of these series constitutes a necessary and sufficient stability condition, which generalizes the analogous condition for 1-D systems.