Exponentially stable solution of mathematical model of agents dynamics on time scales

Abstract

This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consensus for any time scale basing on the Grönwall inequality. We give some examples illustrating the obtained results.

Exponential Stability of Integro-Differential Volterra Equation on Time Scales

“…The readers are referred to the books [4,5] for the fundamentals of the time scales. Basic qualitative and quantitative results on Volterra equations on time scales with applications can be found in [10][11][12], and in the discrete case in [6,[13][14][15]18], and the references cited therein. There is an interesting topic in mathematical modelling to study consensus on time scales.…”

“…There is an interesting topic in mathematical modelling to study consensus on time scales. This problem concerns on stability, in particular exponential stability, of considered equation (see, for example, [8,9,16,18]).…”