Finite Spectrum Assignment for Completely Regular Differential-Algebraic Systems with Aftereffect

Abstract

For linear autonomous completely regular differential-algebraic systems with commensurable delays in the state and control, we study the problem of constructing a state feedback that ensures a finite spectrum for the closed-loop system. We propose criteria for spectral reducibility and weak spectral reducibility whose proofs contain the synthesis schemes of appropriate controllers. Several illustrative examples are given.