‘Small delay-term’ type stabilizability criteria for linear systems with delay

Abstract

Stabilizability criteria and a method of stabilization for a linear constant system with time-delay by linear feedback of the internal variables are considered. If we could assign at will the poles of the system from which the delay-term is removed and the ‘size’ of the term is small enough, then the closed-loop system would become stable. Several stabilizability criteria are derived based on this intuitive idea. The features of the results are above all their simplicity and tractability. Stabilizability can be checked simply by evaluating the norm of a matrix involving the delay-term and some parameters. Moreover, if we can get information on the delay, an estimate of the transient behaviour of the closed-loop system can be obtained.