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Keywords:
Gronwall's inequality; perturbed system; practical $h$-stability
Gronwall's inequality; perturbed system; practical $h$-stability
Summary:
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.
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