A Stability Test for Control Systems with Delays Based on the Nyquist Criterion

The aim of this contribution is to revise and extend results about stability and stabilization of a retarded quasipolynomial and systems obtained using the Mikhaylov criterion in our papers earlier. Not only retarded linear time-invariant time-delay systems (LTI-TDS) are considered in this paper; neutral as well as distributeddelay systems are the matter of the research. A LTI-TDS system of retarded type is said to be asymptotically stable if all its poles rest in the open left half plane. Asymptotic stability of neutral systems described by its spectrum is not sufficient to express the notion of stability at whole since neutral LTI-TDS are sensitive to infinitesimal delay changes. This yields the concept of so called strong stability involving this fact. Moreover, stability can not be studied using the characteristic quasipolynomial when distributed delays in either input-output or internal relation appear in a model. The contribution transforms the formulation of the Mikhaylov criterion (the argument principle) into the language of the Nyquist criterion for the open loop of a control system. The classical simple feedback loop is considered. Illustrative examples are presented to clarify the results. Keywords—Stabilization, stability, time delay systems, Nyquist criterion, argument principle, distributed delays.