THE EFFECT OF SMALL TIME-DELAYS ON THE CLOSED-LOOP STABILITY OF BOUNDARY CONTROL-SYSTEMS

It has been observed that for many stable feedback systems, the introd uction of arbitrarily small time-delays into the loop causes instabili ty. In this paper we present a systematic treatment of this phenomenon for a large class of boundary control systems which allows for in-spa n control. Our approach is based on a combination of input-output meth ods and modal analysis. We give a number of sufficient conditions for robustness/nonrobustness of closed-loop input-output stability with re spect to delays. Our framework includes a large class of ill-posed sys tems, i.e., systems whose open-loop transfer function is unbounded on any right half-plane. We then analyze the relationship between the pol es of the transfer function and the exponential modes of the underlyin g boundary-value problem to derive internal stability properties from external ones.