INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 82:1158–1179 Published online 22 December 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2805 Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay Oreste S. Bursi 1, ∗, † , David P. Stoten 2 , Nicola Tondini 1 and Leonardo Vulcan 1 1 Department of Mechanical and Structural Engineering, University of Trento, Via Mesiano 77—Povo (TN) 38123, Italy 2 Department of Mechanical Engineering, University of Bristol, Bristol BS8 1TR, U.K. SUMMARY Adaptive control techniques can be applied to dynamical systems whose parameters are unknown. We propose a technique based on control and numerical analysis approaches to the study of the stability and accuracy of adaptive control algorithms affected by time delay. In particular, we consider the adaptive minimal control synthesis (MCS) algorithm applied to linear time-invariant plants, due to which, the whole controlled system generated from state and control equations discretized by the zero-order-hold (ZOH) sampling is nonlinear. Hence, we propose two linearization procedures for it: the first is via what we term as physical insight and the second is via Taylor series expansion. The physical insight scheme results in useful methods for a priori selection of the controller parameters and of the discrete-time step. As there is an inherent sampling delay in the process, a fixed one-step delay in the discrete-time MCS controller is introduced. This results in a reduction of both the absolute stability regions and the controller performance. Owing to the shortcomings of ZOH sampling in coping with high-frequency disturbances, a linearly implicit L-stable integrator is also used within a two degree-of-freedom controlled system. The effectiveness of the methodology is confirmed both by simulations and by experimental tests. Copyright 2009 John Wiley & Sons, Ltd. Received 18 March 2009; Revised 21 October 2009; Accepted 26 October 2009 KEY WORDS: adaptive control; non-linear dynamics; discrete-time systems; time delays; linearly implicit L-stable integrators ∗ Correspondence to: Oreste S. Bursi, Department of Mechanical and Structural Engineering, University of Trento, Via Mesiano 77—Povo (TN) 38123, Italy. † E-mail: oreste.bursi@ing.unitn.it Contract/grant sponsor: Department of Mechanical and Structural Engineering (DIMS) Contract/grant sponsor: Department of Mechanical Engineering of the University of Bristol Copyright 2009 John Wiley & Sons, Ltd.