Stability of state delay systems based on a Lyapunov functional

Abstract

Stability of state delay systems is discussed by investigating properties of a Lyapunov functional. Firstly finite characterization of a Lyapunov functional equation for state delay systems is proposed. The finite characterization can be computed using a matrix exponential function, while conventional computation has been relied on numerical approximations. Secondly based on the finite characterization, a stability condition for state delay systems with unknown but bounded constant delay is proposed.