Stability analysis of quasilinear systems on time scale based on a new estimation of the upper bound of the time scale matrix exponential function

Abstract

In this paper, the stability of quasilinear systems on time scale is analyzed based on a new estimation of the upper bound of the time scale matrix exponential function. First, some new upper bounds for the norm of the matrix exponential function $e_A(t,t_0)$ are derived, where $A$ is a regressive square matrix, $t,t_0\in T$, $T$ being a time scale. The matrix exponential function generalizes the usual matrix exponential as well as the integer power of a matrix. It is shown that the obtained bounds are more accurate compared to the existing bounds of the norm of the matrix exponential function. One of the upper bounds is then used for stability investigation of quasilinear systems evolving on arbitrary time domains.