Stability properties of Smith dead-time compensator controllers

The special stability properties of SISO systems incorporating Smith dead-time compensator controllers are investigated. It is shown that the conventional approach to the design of such systems may lead to practical instabilities. Necessary conditions for practical stability and sufficient conditions guaranteeing certain sensitivity and relative stability properties are stated and proven. The inaccuracies in the models are measured by means of an ' ignorance function '. Sufficient conditions expressed in terms of this function, from which conservative estimates on allowed mismatches in the models may be found, are stated. Illustrative examples demonstrating the main results are presented.