On finite time instability of continuous time delay systems

Finite time instability for linear continuous time-delay systems was investigated in this paper. The novel Lyapunov-like functions were used in the analysis. The functions do not need to fulfill the following conditions: being positive definite on the whole state space domain and possessing negative derivatives along the system trajectories. These functions were previously used for the development of both the delay-dependent and delay-independent sufficient conditions for the investigation of the finite time stability of control systems. However, the reported conditions cannot be used for the precise calculation of the instant when the system trajectory leaves the prescribed boundaries. In this paper, a novel concept of finite time instability was introduced to solve this problem. Numerical examples were used to additionally clarify the procedure.