Uniformly finally bounded solutions to systems of differential equations with variable structure and impulses

Abstract

We study nonlinear non-autonomous systems of ordinary differential equations with variable structure and impulses. The consecutive changes on right-hand sides of this system and the impulsive effects on the solution of the corresponding initial problem take place simultaneously at the moment when the solution cancels the switching functions. We find sufficient conditions for the uniform final boundedness of solutions. These results are obtained using a suitable variation of the Lyapunov second method.

Keywords

• Variable structure
• impulses
• switching functions
• uniformly finally bounded solutions