Applications of a New-Type Stability Theorem

Based on the author's previous work in the literature, a new-type stability theorem for general retarded dynamical systems is presented. After three preliminary lemmas are established, linear systems with multiple time-varying delays are considered to show the applications of the new-type stability theorem and the proposed new stability analysis technique. The delay-independent and delay-dependent stability criteria are established for the systems under consideration, respectively. Unlike some results in the literature, all of the established results do not depend on the derivatives of time-varying delays. Therefore, the established results are suitable for the cases with very fast time-varying and bounded delays.