The widely known LQG design method for linear time invariant SISO plants may lead under certain circumstances to closed loop systems that have no stability margins; their sensitivity is infinite and the resulting system is non-causal. We refer to such systems as inadmissible ones. This rather surprising phenomenon is analysed in the paper and is shown to be a generic property, depending on structural features of the plant, noises and criteria involved. Necessary and sufficient conditions guaranteeing admissibility of LQG design, in both the frequency and the time domains, are presented and proved. These conditions enable an a priori detection of such possible ‘traps’ in the LQG method. Although the paper focuses on LQG, some of the results are shown to be of wider applicability. It is shown that the common combination observer-static state feedback is inadmissible if input derivatives are used by the observer. The conditions derived in the paper are used to identify suboptimal methods, developed for other purposes, by which the causality problem may be avoided. A new suboptimal method is suggested and the stability properties of suboptimal designs are discussed. In addition some apparent ambiguities regarding the stability properties of singular observation LQG designs are clarified by means of the results derived in the paper.
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