International journal of systems science vol:34 issue:8-9 pages:543-551
It is well known that the stability of the Smith Predictor control scheme is sensitive with respect to delay uncertainties. We analysed the effect of delay mismatches on the closed-loop stability and derived various stability/instability characterizations. Thereby, it was assumed that the desired closed-loop transfer function was proper but not necessarily strictly proper. This may induce a sensitivity of stability with respect to infinitesimal delay mismatches and make the scheme practically unstable. We explained the instability mechanism and derived the necessary and sufficient robustness conditions using two different approaches. Under the assumption of practical stability, we then characterized the maximal delay mismatch such that stability was maintained and discussed a numerical example. Both SISO and MIMO systems are considered.