Implementation of Systems Identification by Subspace Using C/C++


  • Santos Miranda Borjas Universidade Federal do Rio Grande do Norte, Av. Senador Salgado Filho, Rio Grande do Norte- Brasil
  • Guilherme Pillon de C. A. Pessoa Universidade Federal do Rio Grande do Norte, Av. Senador Salgado Filho, Rio Grande do Norte- Brasil



Subspace Identification, Deterministic Systems, C/C


Nowadays, an engineer’s work consists more and more of obtaining mathematical models of the studied processes. Great part of the literature referring to system identification deals with how to find polynomial models as Prediction Error Methods (PEM) and Instrumental Variable Methods (IVM). In case of complex systems, the state space model appears as an alternative to PEM and IVM models. For multivariable systems, these methods provide reliable state space models directly from input and output data. As systems of large dimensions are usually found in industry, the application of subspace identification algorithms in this field is very promising. Currently the subspace
identification models Multivariable Output Error State sPace (MOESP) and Numerical algorithms for Subspace State Space System IDentification (N4SID), are topic of study. The objective of this work is to implement the N4SID algorithm in C/C ++ and in Matlab to identify discrete systems invariant in time operating in open loop, comparing these in relation to performance and processing time.


Borjas,S.D., Garcia, C. Subspce identification using the integration of MOESP and N4SID methods applied to the Shell benchmark of a distillation TEMA-Tend.Mat.Apl.Comput., Vol. 12, (2011), 183-194.

Borjas, S.D.M. Garcia, C. Modelagem de FCC usando métodos de identificação por predição de erro e por subespaços. IEEE América Latina, Revista virtual - na Internet,2, No. 2, (2004), 108-113.

De Moor, B., Van Overschee P. and Favoreel, W. Algorithms for subspace state space system identification - an overview. In B. Datta (Ed.), Applied and computational control, signal and circuits, Vol. 1, pp. 247-311. Birkhauser: Boston (Chapter 6), 1999.

Favoreel, W., De Moor, B. and Van Overschee, P. Subspace state space system identification for industrial processes. Journal of Process Control,10, No.3, (2000), 149-155.

Roberto, P.; Kurka, G.; Cambraia, H. Application of a multivariable input-output subspace identification technique in structural analysis, Journal of Sound and Vibration,312, No. 3, (2008), 461-47.

Van Overschee, P.; De Moor, B. Subspace Identification for Linear Systems: Theory, Implementation, Applications, Dordrecht: Kluwer Academic Publishers, 1996.

Van Overschee, P.; De Moor, B. Closed loop subspace systems identification, em "Proc. 36th IEEE Conference on Decision and Control, pp. 1848-1853, San Diego, 1997.

Verhaegen, M. Application of a subspace model identification technique to identify LTI systems operating in closed loop, Automatica,29, No 4, (1993), 1027-1040.

Verhaegen, M.; Dewilde, P. Subspace model identification. part i: the output-error state-space model identification class of algorithms, International Journal of Control,56, No. 1, (1992), 1187-1210.

Akaike, H. Information theory and an extension of the maximum likelihood principle. In: Second International Symposium on Information Theory, Budapest, Hungary. Petrov, B.N.; Csaki, F.; (Eds.), pp. 267-281, 1973.

Borjas, S.D.M. Estudo da identificação por subespaços em malha aberta e fechada e proposta de novos algoritmos, Tese de Doutorado, POLI, USP, São Paulo, SP, 2009.



How to Cite

Miranda Borjas, S., & A. Pessoa, G. P. de C. (2018). Implementation of Systems Identification by Subspace Using C/C++. Selecciones Matemáticas, 5(01), 74 - 84.