Stability condition of state-delayed systems based on stability-guaranteed discretization

This paper proposes a new delay dependent stability condition for state-delayed systems. This stability condition is based on the discretization of an infinite dimensional kernel of state-delayed systems and provides a check condition when the stability of the discretized system implies state-delayed systems. This check condition is derived using a lifting technique and is given in the form of discrete system H_∞ norm test. The stability condition is shown to converge to the exact stability condition when the order of discretization approaches infinity