Robust output feedback controllers for dynamical systems including delayed perturbations

Abstract

The problem of output feedback stabilization of uncertain dynamical systems including time-varying delay is discussed. Here we assume that the uncertainties satisfy the so-called matching conditions, and that the time-varying delay is any bounded and continuous non-negative function. For such a class of uncertain time-delay systems, we show that under the assumption that the transfer function matrix of the nominal system is strictly feedback positive real, there always exist a class of stabilizing output feedback controllers. We first propose a linear output feedback controller which can guarantee always uniform ultimate boundedness of closed-loop dynamical systems. Furthermore, we modify this linear controller by adding a nonlinear part to obtain a nonlinear output feedback controller which can guarantee always uniform asymptotic stability of closed-loop dynamical systems. As the proposed output feedback controllers are independent of the delay, the results obtained in this paper are applicable to dynamical systems without exact knowledge of the delays, i.e. systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.