Criteria on Exponential Incremental Stability of Dynamical Systems with Time Delay

Incremental stability analysis for time-delay systems has attracted more and more attention for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches the criteria for exponential incremental stability for time-delay systems with continuous or discontinuous right-hand sides. Firstly, the sufficient conditions for exponential incremental stability for time-delay systems with continuous right-hand sides are studied, and several corollaries for specific cases are provided. As for time-delay systems with discontinuous right-hand sides, after expounding the relevant conditions for the existence and uniqueness of the Filippov solution, by using approximation methods, sufficient conditions for exponential incremental stability are obtained. The conclusions are applied to linear switched time-delay systems and Hopfield neural network systems with composite right-hand sides.