Procedure for Constructing Linear Functional Observers

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


In this paper a straightforward procedure, to obtain a linear functional observer with order equal to the dimension of the vector to be estimated, is proposed. Inspired by [3], we have developed a procedure to construct this type of observer in which some significant simplifications have been made and allow computational burden reduction. The procedure developed in this work has the originality and the great advantage that all required matrices are obtained without calculating any generalized inverse. A novel approach which constitutes the coupling of a coordinates transformation and the use of the {1}-inverse property requires only the inversion of a nonsingular matrix. A procedure where all steps are clearly identified is written and a numerical example is provided to illustrate the effectiveness of the observer.
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Linear Functional Observers; State Observers; Estimation

Full Text:



M. Aldeen and H. Trinh. Reduced-order linear functional observers for linear systems. IEEE Proc. Control Theory Appl., 146-5:399–405, 1999.

A. Ben-Israel and T.N.E. Greville. Generalized inverses : theory and applications. 1974.

M. Darouach. Existence and design of functional observers for linear systems. IEEE Trans. Automat. Contr., 45:940–943, 2000.

M. Darouach. Complements to full order observer design for linear systems with unknown inputs. Applied Mathematics Letters, 22-7:1107–1111, 2009.

B. N. Datta. Numerical methods for linear control systems. Academic Press, 2004.

T. Fortmann and D. Williamson. Design of low-order observers for linear feedback control laws. IEEE Trans. Aut. Control, AC-17(3):301–308, 1972.

J. Kautsky and N.K. Nichols. Robust pole assignment in linear state feedback. Int. J. Control, 41:1129–1155, 1985.

B. Larroque, F. Noureddine and F. Rotella, Towards a complete design of linear functional observers, (2008) International Review of Automatic Control (IREACO), 1 (2) pp. 132-142.

D.G. Luenberger. Observers for multivariable systems. IEEE Trans. Aut. Control, 11:190–197, 1966.

D.G. Luenberger. An introduction to observers. IEEE Trans. Aut. Control, 16:596–602, 1971.

Y. Ma, X. Zhong, and Zhang Q. Design of state observer for a class of nonlinear descriptor large-scale composite systems. Int. Jour. of Innovative Computing, Information and Control, 4(8):1967–1975, 2008.

J.B. Moore and G.F. Ledwich. Minimal order observers for estimating linear functions of a state vector. IEEE Trans. Automat. Contr., 20:623–626, 1975.

J. Roman and T. Bullock. Design of minimal order stable observers for linear functions of the state via realization theory. IEEE Trans. on Automatic Control, 1975.

Frédéric Rotella and Pierre Borne. Théorie et pratique du calcul matriciel. Editions Technip, 1995.

K. E. Sobel, E. Y. Shapiro, and A. N. Andry. Eigenstructure assignment. The control Handbook-Levine, (W. S. CRC-IEEE Press, pages 621–633, 1996).

H. Trinh and Q. Ha. Design of linear functional observers for linear systems with unknown imputs. Int. Jour. of Systems Sciences, 31:741–749, 2000.

H. Trinh and J. Zhang. Design of reduced-order scalar function observers. Int. Jour. of Innovative Computing, Information and Control, 1:791–799, 2005.

C.C. Tsui. A new algorithm for the design of multifunctional observers. IEEE Trans. Aut. Control, 30:89–93, 1985.

C.C. Tsui. On the order reduction of linear function observers. IEEE Trans. Aut. Control, 31, 1986.

K. Yamada, D. Z. Gong, Y. Ando, T. Hagiwara, I. Murakami, Y. Imai, and M. Kobayashi. A design method for control system to attenuate output periodic disturbances using disturbance observers for time-delay plants. ICIC Express Letters, 3(3A):507–512, 2009.

K. Yamada, I. Murakami, Y. Ando, T. Hagiwara, Y. Imai, and M. Kobayashi. The parameterization of all disturbance observers. ICIC Express Letters, 2(4):421–426, 2008.

K. C. Yao and C. H. Hsu. Robust optimal stabilizing observer-based control design of decentralized stochastic singularly-perturbed computer controlled systems with multiple time-varying delays. Int. Jour. of Innovative Computing, Information and Control, 5(2):467–477, 2009.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize