Author(s)

Ran Huo¹, Xiaoli Wang²

¹College of Science, Inner Mongolia Agricultural University, Huhhot, China.
²College of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Huhhot, China.

In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.

Time-Delay, Nonlinear Systems, Double Stability, Differential Inequality, Integral Inequality

Huo, R. and Wang, X. (2019) Double Lipschitz Stability for Nonlinearly Perturbed Differential Systems with Multiple Delay. Journal of Applied Mathematics and Physics, 7, 3003-3011. doi: 10.4236/jamp.2019.712210.