Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 299-329

Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics

M. de la Sen

Department of Electricity and Electronics, Faculty of Science and Technology, University of Basque Country, Leioa (Bizkaia), Aptdo, 644 de Bilbao, Spain

Received 26 January 2005

Copyright © 2005 M. de la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single-input single-output (SISO) time-invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous-time type while the other is digital. As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. It also incorporates a relative adaptation dead-zone as a robust stabilization mechanism which prevents against instability in the presence of a common class of unmodeled dynamics and bounded noise.