In this paper, we examine a design method for modified Smith predictor for non-minimum-phase time-delay plants with multiple time-delays. The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time-delay, and several papers on the modified Smith predictor have been published. The parametrization of all stabilizing modified Smith predictors for minimum-phase time-delay plants is obtained by Yamada and Matsushima. Yamada et al. expand the result by Yamada and Matsushima and propose the parametrization of all stabilizing modified Smith predictor for non-minimum-phase systems. In some cases, the plant includes multiple time-delays. For minimum-phase timedelay plants with multiple time-delays, the parametrization of all stabilizing modified Smith predictors is solved by Yamada and Takenaga. However, they do not examine the parametrization of all stabilizing modified Smith predictors for non-minimum-phase time-delay systems with multiple time-delays. The purpose of this paper is to expand the result by Yamada and Takenaga and to propose the parametrization of all stabilizing modified Smith predictors for non-minimum-phase time-delay plants with multiple time-delays.

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In this paper, we consider the robust stability condition for single-input/single-output time-delay plants with new class of uncertainties. First of all, we define a class of uncertainties to be considered. The necessary and sufficient robust stability condition for time-delay plants with such class of uncertainties is presented. The relation between the time-delay plant and the nominal time-delay plant to satisfy the robust stability condition is clarified. By using this relation, we will show the necessary and sufficient robust stability condition for the time-delay plant with varying number of right half plane poles.

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