Stability analysis of state-delay systems based on the characterization of state-transition operator

Stability conditions for state-delay systems are derived based on the norm of semigroup, which describes the transition of the internal state. Introducing an exact calculation method of the semigroup norm, the conditions for the internal stability and the marginal stability are characterized by non-singularity of a transcendental function. The conditions depend on the existence of time interval such that the semigroup turns to a contraction map and enable us to approach the necessary and sufficient condition by extending the interval. The feature of proposed method is discussed with numerical examples.