Synthesis of damping controllers for the solution of completely regular differential-algebraic delay systems

Abstract

For linear autonomous completely regular differential-algebraic delay systems, we develop methods for synthesizing state feedback controllers that simultaneously provide solution damping and finite spectrum assignment in the closed-loop system. We prove necessary and sufficient conditions for the existence of such controllers defining finite- and infinite-time controls depending on the system parameters (complete 0-controllability and 0-controllability criteria, respectively). The proofs are of constructive character and allow one to synthesize the corresponding controller for every system. An illustrative example is given.