Adaptive observers for structurally perturbed positive real delay systems

Abstract : The aim of this investigation is to construct an adaptive observer for a class of muiltivariable delay systems having a known exogenous input and a structured perturbation with an unknown constant parameter such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates and convergence of the estimator error. We illustrate our approach with a multivariable delay example for which we obtain convincing numerical results.