Predictor based control for linear systems with both state and input delays

In this paper we develop a predictor based controller for linear systems with state and input delays. 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. When the past state and input information is available within a moving time window, it is shown that this 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 redundant computation and simplify the predictor equation for practical implementation. It is demonstrated that the state prediction becomes exact, i.e., the prediction error is zero in a finite time. In order to construct a predictor feedback control law, we show that the spectrum of the closed-loop delay system under a proposed predictor feedback control is equal to the spectrum of an equivalent delay system without input delay and under the nominal state feedback control. The theoretical derivation is verified through numerical examples.