Why Finite-Time Stability is So Special: Operator Norm and Multivariate Eigenvalue Problem Behind the Curtain

In this paper, the problem of finite-time stability of linear systems with single delay is considered. A set of conditions equivalent to the definition are derived. These conditions are in the form of continuous multivariate eigenvalue problem or Karush-Kuhn-Tucker conditions. By these conditions, finite-time stability of linear time delay system can be checked numerically. A numerical example is given to illustrate the potentialities of these conditions.