An Approach to Discrete System Identification Based on Matrix Zero Divisors

The purpose of this work was to consider a deterministic approach to parametric identification of linear discrete systems based on matrix zero divisors. We determined the conditions for the solvability of the identification problem. Moreover, we formulated the identifiability criterion and built the solution formula (identification algorithm). By numerical examples we demonstrated the possibilities of the approach.

References

[1] Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., Ryabchenko V.N., Timakov S.N., Cheremnykh E.A. Identification of the position of an equilibrium attitude of the International Space Station as a problem of stable matrix completion. Journal of Computer and Systems Sciences International, 2012, vol. 51, no. 2, pp. 291-305. DOI: 10.1134/S1064230712010133 Available at: https://link.springer.com/article/10.1134/S1064230712010133

[2] Zubov N.E., Mikrin E.A., Ryabchenko V.N., Timakov S.N. The use of an adaptive bandpass filter as an observer in the control loop of the International Space Station. Journal of Computer and Systems Sciences International, 2012, vol. 51, no. 4, pp. 560-572. DOI: 10.1134/S1064230712030124 Available at: https://link.springer.com/article/10.1134/S1064230712030124

[3] Aarts R.G. System identification and parameter estimation. Twente University, 2012.

[4] Bedoui S., Ltaief M., Abderrahim K. New results on discrete-time delay systems identification. Int. Journal of Automation and Computing, 2012, vol. 9, no. 6, pp. 570-577. DOI: 10.1007/s11633-012-0681-x Available at: https://link.springer.com/article/10.1007/s11633-012-0681-x

[5] Graupe D. Identification of systems. Krieger Pub. Co., 1976. 288 p.

[6] Misrikhanov M.Sh., Ryabchenko V.N. Algebraic and matrix methods in theory of linear MIMO-systems. Vestnik IGEU, 2005, no. 5, pp. 196-240 (in Russ.).

[7] Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., Oleynik A.S., Ryabchenko V.N. Terminal bang-bang impulsive control of linear time invariant dynamic systems. Journal of Computer and Systems Sciences International, 2014, vol. 53, no. 3, pp. 430-444. DOI: 10.1134/S1064230714030174 Available at: https://link.springer.com/article/10.1134/S1064230714030174