Stability and Boundedness of Solutions to Some Non-autonomous Multidimensional Nonlinear Systems
Abstract
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the known techniques provide computationally intensive and conservative stability criteria in this field and frequently fail to estimate the regions of boundedness/stability of solutions to the corresponding systems. Recently, we outlined a new approach to this problem which is based on the analysis of solutions to a scalar auxiliary equation bounded from the above time histories of the norms of solutions to the original system. This paper develops a novel technique casting the auxiliary equation in a modified form which extends the application domain and reduces the computational hamper of our prior approach. Consequently, we developed more general boundedness/stability criteria and estimated trapping/stability regions for some multidimensional nonlinear systems with nonperiodic time-dependent coefficients that are common in various application domains. This let us to assess in target simulations the extent of boundedness/stability of some multidimensional, nonlinear and time-varying systems which were intractable with our prior technique.
Cite
@article{arxiv.2012.13674,
title = {Stability and Boundedness of Solutions to Some Non-autonomous Multidimensional Nonlinear Systems},
author = {Mark A. Pinsky},
journal= {arXiv preprint arXiv:2012.13674},
year = {2022}
}
Comments
29 pages. The new version of this paper adds a motivation example, see section 1.2, and significantly updates section 3. Other minor additions have been made throughout. A typo in the previous version of this paper was corrected. This paper is accepted for publication in J. Mathematical Problems in Engineering, 2022