Existence and uniqueness of the solutions of continuous nonlinear 2D Roesser Models: The globally Lipschitz case
Existence and uniqueness of the solutions of continuous nonlinear 2D Roesser Models: The globally Lipschitz case
复制标题
连续非线性二维 Roesser 模型解的存在唯一性：全局 Lipschitz 案例
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Yeganefar
中科院分区：
文献类型：
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作者：
R. David;Nima Yeganefar;Francisco J. Silva;O. Bachelier;N. Yeganefar
本通讯涉及多维系统领域中一个长期存在的开放问题。研究了非线性连续二维Roesser模型解的存在唯一性问题。证明了若描述Roesser模型的函数是全局Lipschitz的，则在给定的初始条件下，存在唯一的连续解.几个例子表明，这些假设不能轻易放松。这是分析非线性Roesser模型稳定性和镇定性的重要依据。
This communication deals with a long standing open problem in the field of multidimensional systems. We tackle the question of the existence and uniqueness of the solutions for nonlinear continuous 2D Roesser models. It is proved that if the function describing the Roesser model is globally Lipschitz, a continuous solution exists and is unique for a given set of initial conditions. Several examples show that these assumptions cannot be easily relaxed. This is an important basis that is crucial to the analyzes of stability and stabilization of nonlinear Roesser models.