Mathematical Problems in Engineering
Volume 2004 (2004), Issue 2, Pages 109-131

Adaptive stabilization of continuous-time systems through a controllable modified estimation model

M. de la Sen

Instituto de Investigación y Desarrollo de Procesos (IIDP), Departamento de Ingeniería de Sistemas y Automática, Facultad de Ciencias, Universidad del Pais Vasco, Campus de Bizkaia, Aptdo 644 de Bilbao, Bilbao 48080, Spain

Received 9 October 2003; Revised 9 February 2004

Copyright © 2004 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 presents an indirect adaptive control scheme of continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modifieddiagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of an explicit hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present.