In George Zames Special Issue of the Int. J. of Robust and Nonlinear Control, 10(11-12):909–929, Sep. 2000. Multiple Model Adaptive Control, Part 1: Finite Controller Coverings * Brian D. O. Anderson ¶ , Thomas S. Brinsmead ¶ , Franky De Bruyne ¶ , Jo˜aoHespanha ‡ , Daniel Liberzon § , A Stephen Morse § September 2000 ¶ RSISE, Australian National University, Canberra ACT 0200, Australia ‡ EE-Systems, Univ. of Southern California, Los Angeles, CA 90089-2563 § Dept. Elec. Eng., Yale University, New Haven, CT 06520-8267, USA Abstract We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild as- sumptions on the uncertainty set of linear time-invariant plant models, it is possible to determine a finite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the finite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately band- and time-limited transfer functions is approximately finite-dimensional. Key Phrases- Band-Limited, epsilon-Entropy (ǫ-Entropy), Finite Covering, Multiple Model Control, Time-limited, Vinnicombe Metric * This research was supported by the Office of Naval Research, grant numbers N00014-97-1-0946 and N00014-98-1- 0535. The authors would also like to acknowledge the support of the NSF, AFOSR and DARPA.