Linear systsems with rational distributed delay: Reduction and stability

A reduction method for the class of distributed delay systems with rational kernel is studied. It transforms the delay system to one with fixed crisp delays. Applications in stability analysis and realization with integrators and (fixed) delay lines is shown. The second part illustrates the use of algebraic methods to obtain necessary and sufficient stability conditions for a subclass of systems. These conditions are based on the known NASC for the scalar delay system and involve the location of a finite number of generalized poles in C.