Stability of perturbed dynamic system on time scales with initial time difference

Abstract

The behavior of solutions of a perturbed dynamic system with respect to an original unperturbed dynamic system, which have initial time difference, are investigated on arbitrary time scales. Notions of stability, asymptotic stability, and instability with initial time difference are introduced. Sufficient conditions of stability properties are given with the help of Lyapunov-like functions.

The relation between the existence of bounded global solutions of the differential equations and equations on time scales

“…The optimal control problems for the systems of ordinary differential equations and the corresponding dynamical equations on time scales were considered in [4,6,12]. The stability of perturbed dynamic system on time scales was addressed in [15] using the appropriate analogs of Lyapunov functions .…”