Title :
Improved Razumikhin-Type Theorem for Input-To-State Stability of Nonlinear Time-Delay Systems
Author :
Chongyang Ning ; Yong He ; Min Wu ; Jinhua She
Author_Institution :
Sch. of Inf. Sci. & Eng., Central South Univ., Changsha, China
Abstract :
This note describes a Lyapunov-Razumikhin function with an indefinite derivative that can be used to determine the input-to-state stability (ISS) of a nonlinear time-delay system. First, an extended comparison principle for estimating the solution of a differential inequality with an upper bound that is not (semi)negative definite is presented. Then, that principle and a Lyapunov-Razumikhin function with an indefinite derivative are employed to derive an ISS criterion. Finally, two examples show the effectiveness of our method and its superiority over others.
Keywords :
delay systems; nonlinear control systems; stability; Lyapunov-Razumikhin function; Razumikhin-type theorem; differential inequality; indefinite derivative; input-to-state stability; nonlinear time-delay systems; Asymptotic stability; Educational institutions; Estimation; Stability criteria; Thermal stability; Upper bound; Indefinite derivative; Lyapunov–Razumikhin function; input-to-state stability (ISS); nonlinear systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2013.2297183
