Lyapunov stability of two-dimensional digital filters with overflow nonlinearities
Lyapunov stability of two-dimensional digital filters with overflow nonlinearities
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DOI：
10.1109/81.668870
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发表时间：
1998-05
影响因子：
5.1
通讯作者：
Derong Liu
中科院分区：
文献类型：
--
作者：
Derong Liu
本文利用Lyapunov第二方法建立了具有一般溢出非线性的零输入二维Fornasini-Marchesini状态空间数字滤波器平凡解全局渐近稳定的充分条件。建立了具有溢出非线性的二维Fornasini-Marchesini第二模型零解的全局渐近稳定性结果。几类Lyapunov函数被用来建立目前的结果，包括向量范数和二次型。当考虑二次型Lyapunov函数时，本文的结果包含了正定矩阵可用于产生具有溢出非线性的2-D数字滤波器的Lyapunov函数的充要条件。
In this paper, the second method of Lyapunov is utilized to establish sufficient conditions for the global asymptotic stability of the trivial solution of zero-input two-dimensional (2-D) Fornasini-Marchesini state-space digital filters which are endowed with a general class of overflow nonlinearities. Results for the global asymptotic stability of the null solution of the 2-D Fornasini-Marchesini second model with overflow nonlinearities are established. Several classes of Lyapunov functions are used in establishing the present results, including vector norms and the quadratic form. When the quadratic form Lyapunov functions are considered, the present results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for 2-D digital filters with overflow nonlinearities.