Hybrid Predictor for Unstable Delayed Systems

Delays are known to complicate closed-loop stability analysis and controller design. In the present work, the problem of the stabilization and control of a particular class of linear systems with several real/complex conjugate stable poles and one unstable pole with delay in the direct path is considered. In this work, a methodology is proposed to design a hybrid predictor that consists of continuous and discrete signals to address systems with delay. The proposed hybrid predictor provides a continuous estimation of variables of interest, which is an important consideration, in contrast to the control strategies based on a discrete domain approach. The key point of this proposal is to guarantee the existence of the hybrid predictor, without any restriction on the delay size, when the delay is not divisible by an integer for an appropriate implementation of the sampling period, as in the traditional discrete approach. Furthermore, the proposed methodology is not restricted by the order of the plant, its instability or the size of the delay. The effectiveness of the results is illustrated by numerical simulations performed on academic examples.