Asymptotic Stabilization of Time-Delay Systems via Vector Lyapunov Functions

In this essay, the issue of asymptotically stable for a class of time-delay nonlinear systems is the main topic. Firstly, an asymptotic stability theorem is proposed by adjusting Lyapunov Razumikhin (L-R) lemma using the vector Lyapunov function method. A control method and a set of parameter conditions are suggested for time-delay nonlinear systems using this theorem to ensure asymptotic convergence. Moreover, the use of this theory additionally decreases the processing burden by avoiding a sizable number of inequality calculations. At last, an example of the simulation is provided to prove the efficacy and safety of our suggested algorithm.