Stability issues and program support for time delay systems in state over finite time interval

The main concept of this paper is focused on finding finite time intervals, where time delay system with delay in state is stable. The problem is observed from singular values and fundamental matrix point of view. Although, there are some papers covering practical stability problems for time delay systems with delay in state, it was observed lack of exploring it, by comparing different approaches such as matrix measure, singular values and parameter solution. It is applied Bade approximation for eliminating time delay from the system of second order, and it is shown program support for solving general problem for time delay systems with delay in state. After presented theorems for both approaches, it is shown the numerical example. The desired stability time interval is obtained by using singular values point of view, and after that system is analyzed by using matrix measure. The given result matched the desired interval, and program support for general solution is developed by using Maple programming language. (C) 2019 Elsevier B.V. All rights reserved.