2021/01/25 by Gerson Portilla, Portilla, Gerson, Irina V. Аlexandrova +3
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Differential Equations Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2101.10365
openalex publication_date 2021/01/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we present estimates for solutions and for the attraction\ndomain of the trivial solution for systems with delayed and nonlinear weighted\nhomogeneous right-hand side of positive degree. The results are achieved via a\ngeneralization of the Lyapunov-Krasovskii functional construction presented\nrecently for homogeneous systems with standard dilation. Along with the\nclassical approach for the calculation of the estimates within the\nLyapunov-Krasovskii framework, we develop a novel approach which combines the\nuse of Lyapunov-Krasovskii functionals with ideas of the Razumikhin framework.\nMore precisely, a lower bound for the functional on a special set of functions\ninspired by the Razumikhin condition is constructed, and an additional\ncondition imposed on the solution of the comparison equation ensures that this\nbound can be used to estimate all solutions in a certain neighbourhood of the\ntrivial one. An example shows that this approach yields less conservative\nestimates in comparison with the classical one.\n