On degeneracy of functional-differential equations

Abstract

Publisher Summary This chapter discusses degeneracy of functional differential equations. The conjecture that linear difference-differential equations with constant coefficients are point-wise complete was presented in an earlier paper on controllability of delay-differential systems. At that time, it was known that nonautonomous systems need not to be point-wise complete. If a certain matrix has full rank, then contrary to the situation in the case of ordinary differential equations, this is sufficient for ℝ n null-controllability of a linear delay system. To make this rank condition also necessary for ℝ n null-controllability, one has to assume point-wise completeness of the system.