2014/03/23 by Myroslav Sparavalo, Sparavalo, Myroslav
Engineering · Physics and Astronomy · #34A60 #34D23 #34D35 #34D45 #37C70 #37C75 #53C12 #55R10 #57R30 #93D05 #93D20 #Control and Stability of Dynamical Systems #Elasticity and Wave Propagation #FOS: Electrical engineering #Quantum chaos and dynamical systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1403.5761
openalex publication_date 2014/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
The objective of the research is to develop a general method of constructing Lyapunov functions for non-linear non-autonomous differential inclusions described by ordinary differential equations with parameters. The goal has been attained through the following ideas and tools. First, three-point Poincare strategy of the investigation of differential equations and manifolds has been used. Second, the geometric-topological structure of the non-linear non-autonomous parametric differential inclusions has been presented and analyzed in the framework of hierarchical fiber bundles. Third, a special canonizing transformation of the differential inclusions that allows to present them in special canonical form, for which certain standard forms of Lyapunov functions exist, has been found. The conditions establishing the relation between the local asymptotical stability of two corresponding particular integral curves of a given differential inclusion in its initial and canonical forms are ascertained. The global asymptotical stability of the entire free dynamical systems as some restrictions of a given parametric differential inclusion and the whole latter one per se has been investigated in terms of the classificational stability of the typical fiber of the meta-bundle. There have discussed the prospects of development and modifications of the Lyapunov second method in the light of the discovery of the new features of Lyapunov functions.