Finite Lyapunov Stability Test for a Class of Linear Systems With Pointwise and Distributed Delays

This contribution presents two exponential stability criteria (necessary and sufficient conditions) for linear systems with multiple pointwise and distributed delays. An important property is that the stability test requires a finite number of mathematical operations. The results are given in terms of the delay Lyapunov matrix and the fundamental matrix of the system. The exact construction of these matrices is possible for systems with delays multiple of a basic one and distributed delays with kernels expressed in the same finite basis as their derivative.