The Nyquist criterion for LTI time-delay systems

Abstract

This paper extends results about stability and stabilization of a retarded quasipolynomial obtained using the Mikhaylov criterion earlier. Retarded quasipolynomials appear as numerators and denominators of linear time-invariant time-delay systems (LTI-TDS). A LTI-TDS system of retarded type (destitute of distributed delays) is said to be stable if all roots of its characteristic quasipolynomial are located in the open left-half complex plane. The contribution transforms the formulation of spectrum assignment of a characteristic quasipolynomial into the language of the Nyquist criterion for the open loop of a control system. Again, the argument principle is utilized to derive generalized Nyquist criterion for LTI-TDS. Stability measures related to the criterion are discussed with the specifications for LTI-TDS. An illustrative example is presented to illuminate the results.