A State Predictor for Multivariable Systems Including Multiple Delays in Each Output Path

Various practical systems include time delays due to measurement and computational delays, and transmission and transport lags. In this paper, the authors propose a novel state predictor for a certain class of multivariable systems including multiple output delays. The predictor consists of full-order observers estimating past state from each delayed output and finite interval integrators compensating the effect of the delays using state transition equations. State prediction error converges to zero at an arbitrary rate, which can be determined by choosing a finite number of poles of the full-order observers. In this predictor, the distance to instability of the state transition matrix is not affected by the delays. This means that large delays have no influence on the numerical stability, whereas that of a conventional observer highly depends on the delays. Numerical examples for an integral process and an unstable process demonstrate the effectiveness of the proposed predictor.