Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 123751, 12 pages
Research Article

Stabilizability and Disturbance Rejection with State-Derivative Feedback

Departamento de Engenharia Elétrica, Faculdade de Engenharia de Ilha Solteira, Universidade Estadual Paulista (UNESP), 15385-000 Ilha Solteira, SP, Brazil

Received 23 September 2010; Accepted 9 December 2010

Academic Editor: Fernando Lobo Pereira

Copyright © 2010 Manoel R. Moreira et al. 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.


In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state-derivative signals than the state signals. This paper shows that (i) linear time-invariant plants given by the state-space model matrices { 𝐴 , 𝐵 , 𝐶 , 𝐷 } with output equal to the state-derivative vector are not observable and can not be stabilizable by using an output feedback if d e t ( 𝐴 ) = 0 and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, considering d e t ( 𝐴 ) 0 , and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state-derivative feedback.