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

Abstract

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.

Keywords

• Time scales
• Leader-following problem
• Grönwall inequality
• Multi-agent systems
• Graph theory