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Practical h -stability behavior of time-varying nonlinear systems

Abir Kicha, Hanen Damak, Mohamed Ali Hammami (2023)

Commentationes Mathematicae Universitatis Carolinae

We deal with the problem of practical uniform h -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform h -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.

Principal solutions and transformations of linear Hamiltonian systems

Ondřej Došlý (1992)

Archivum Mathematicum

Sufficient conditions are given which guarantee that the linear transformation converting a given linear Hamiltonian system into another system of the same form transforms principal (antiprincipal) solutions into principal (antiprincipal) solutions.

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