Stability of Distributed Systems With Feedback via Michailov's Criterion

Stability of Distributed Systems With Feedback via Michailov's Criterion By G. C. REIS* (Manuscript received November 11, 1971) This paper is based on results derived during a stability study of the Saturn V rocket for which it ivas necessary to validate the use of Nyquist's encirclement-counting technique in distributed systems. An outline of the paper is as follows: Certain results concerning the finiteness of the number of zeros of polynomials in s and e' are shown in Theorem 1 and its corollaries. Theorem 2 is a generalization of Michailov's Criterion. Simplifying assumptions, usually valid in practice, yield a simplified test to determine if "encirclement-counting" is a valid stability test [equation (20)]. The results are reformulated for an open-loop analysis. Various aspects of the theory are shown by three examples based on an electrical equivalent of a simple single-engine, liquid-fuel rocket.