Predictor based control of linear systems with state, input and output delays

In this paper we develop a predictor-based controller for linear systems with state, input and output delays. First, a state predictor is developed for state feedback control. This predictor is formulated recursively over the prediction time by partitioning the input delay into sections smaller than the state delays. The partitioning of the input delay ensures that the resulting predictor equation only depends on the past values of the state and input. It is shown that the proposed predictor gives an exact prediction of the future states. This recursive predictor is then reformulated into a cascade form in order to reduce the number of redundant calculations and to simplify the predictor equation for practical implementation. We construct a predictor based state feedback control law and show that the spectrum of the closed-loop time-delay system under the constructed control law is the same as that of an equivalent time-delay system without input delay and under the nominal state feedback control. Therefore, the proposed predictor based solution can stabilize the delay system if a stabilizing state feedback control law exists for the input delay free system. These state feedback results are then extended to the case of delayed output feedback. The theoretical derivation is verified through numerical examples.

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