Convergence criteria for nonhomogeneous linear nonautonomous real‐order time‐delay systems

摘要

Nonhomogeneous linear nonautonomous real‐order time‐delay systems where the coefficient matrices involve time‐varying elements and state variables are dependent on constant multiple delays are considered. Is it possible to determine the limiting behavior of unknown solutions to such systems? We introduce a new comparison inequality, and then by using Laplace transform, we develop some new asymptotic convergence criteria when the coefficient matrices of such systems are constants. We show that it is possible to ensure the limiting behavior of such systems by establishing some new convergence criteria. For an application of interest, we introduce a simple nonhomogeneous linear feedback control and demonstrate that unstable real‐order time‐delay systems can be effectively controlled by using the proposed approach.