##plugins.themes.bootstrap3.article.main##

Hadi S. Amiri Akbar H. Borzabadi Aghileh Heydari

Abstract

We discuss the controllability and observability of time-invariant (continuous time) linear systems with interval coefficients using the notion of being full rank of interval matrices. The most important advantage of the proposed attitude is to consider these two essential concepts, that is, control lability and observability, in interval time-invariant linear systems, which, in turn, may play important roles in the analysis of uncertain systems. Some different definitions on to be full rank of matrices have been utilized to propose different views on the controllability and observability of interval linear systems according to different criteria. Finally, in several control-observation processes, the controllability and observability are evaluated based on the given achievements.

Article Details

Keywords

Controllability;, Observability;, Time-invariant linear systems with interval coefficients.

References
[1] Bhurjee A.K. and Panda, G. Efficient solution of interval optimization problem, Math. Methods Oper. Res. 76 (2012), 273–288.
[2] B. Cheng and J. Zhang, Robust controllability for a class of uncertain linear time-invariant MIMO systems, IEEE Transactions on Automatic Control, 49(11) (2004), 2022–2027.
[3] Chou, J., Chen, S. and Zhang, Q. Robust controllability for linear Uncertain descriptor systems, Linear Algebra and its Applications, 414, (2005), 632–651.
[4] Chui C.K. and Chen, G. Linear systems and optimal control, Springer Verlag Berlin Heidelberg, 1989.
[5] Davison, E.J. Connectiability and structural controllability of composite systems, Automatica, 13 (1977), 109–123.
[6] Heidari M. and Ramezanzadeh, M. Necessary and sufficient conditions for calculus of variations under interval uncertainty, Int. J. Reliability and Safety, 11(1-2) (2017), 1–22.
[7] Heidari, M., Ramezanzadeh, M., Borzabadi A.H., and Fard, O.S. Solutions to fuzzy variational problems: Necessary and sufficient conditions, Int. J. Model. Identif. Control. 28 (2017),187–198.
[8] Ismail, O. and Bandyopadhyay, B. Controllability and observability of linear symmetric interval systems, IEEE International Conference on Control Applications, (1996), 900–903.
[9] Lin, C., Wang, J.L., Yang, G. and Soh, C.B. Robust C-controllability and/or C-observability for uncertain descriptor systems with interval perturbations in all matrices, IEEE Transactions on Automatic Control,
44(9), (1999), 1768–1773.
[10] Lin, C.T. Structural controllability, IEEE Trans. Automatic Control, 19 (1974), 201–208.
[11] Ramezanadeh, M., Heidari, M., Fard O.S. and Borzabadi, A.H. On the interval differential equation: novel solution methodology, Adv. Differ ence Equ. 2015, (2015) 338, 23 pp.
[12] Shary, S.P. On full-rank interval matrices, Numer. Analys. Appl. 7 (2014), 241–254.
[13] Shields, R.W. and Pearson, J.B. Structural controllability of multi-input linear systems, IEEE Trans. Automatic Control, 21 (1976), 203–212.
[14] Wang, K. and Michel, A.N. Necessary and sufficient conditions for the controllability and observability of a class of linear, time-invariant systems with interval plants, IEEE Trans. Automatic Control, 39 (1994),
1443–1447.
[15] Yang, Y. Controllability and observability of a class of linear time invariant systems with interval plants, International Journal of Information and Systems Sciences, 1(1), (2005) 184–192.
How to Cite
AmiriH. S., H. BorzabadiA., & HeydariA. (2020). A different view on controllability and observability of continuous time linear systems with interval coefficients. Iranian Journal of Numerical Analysis and Optimization, 10(1), 107-120. https://doi.org/10.22067/ijnao.v10i1.79654
Section
Research Article