A novel observer-predictor control for uncertain systems with unknown time-varying input and output delays

In this paper, a novel observer-predictor control is proposed to stabilise uncertain systems subject to unknown but bounded arbitrarily-fast time-varying input and output delays. Due to the presence of time-varying model uncertainties and delay mismatches, the separation principle cannot be used to design the observer and control gains separately, which becomes a challenging problem. By applying small gain theory and Lyapunov-Krasovskii functionals (LKF), in combination with Bessel-Legendre inequalities and the Projection Lemma, we develop sufficient conditions based on Linear Matrix Inequalities (LMIs) for control design. As a result, the closed-loop robust performance can be improved whilst satisfying a prescribed decay rate in the closed-loop dynamics at the expense of introducing more LMI decision variables without increasing the complexity of the control scheme. Also, the Extended State Observer (ESO) is integrated in the proposed control scheme to improve the rejection performance of mismatched disturbances. The effectiveness of the proposed method is illustrated by simulation results.