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IMA Journal of Mathematical Control and Information 1998 15(4):363-378; doi:10.1093/imamci/15.4.363
© 1998 by Institute of Mathematics and its Applications
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Reduced-order adaptive control based on the concept of robust strictly positive realness

GIORGIO BARTOLINI , ANTONELLA FERRARA  and A. V. SAVKIN 

Department of Communication, Computer and System Sciences, University of Genova Via Opera Pia 11A, 16145 Genova, Italy
Department of Electrical Engineering, Australian Defence Force Academy Campbell, 2600, Australia

In this work, we consider uncertain systems which present a separation between the ‘slow’ and the ‘fast’ dynamics. The fast dynamics, in particular, are required to satisfy a suitable frequency inequality, which characterizes the region to which the ‘fast poles’ are assumed to belong. By suitably combining the concept of a robust strictly positive real transfer function, introduced in this paper, which that already known of almost strictly positive realness, it is possible to design a reduced-order adaptive control scheme characterized by globally asymptotically stable behaviour of the output error, internal stability, and boundedness of the controller parameters. Moreover, for some class of reference signals, the asymptotic tracking of the reference is guaranteed.

Keywords: Adaptive control; robustness; strictly positive realness; stability.


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