Abstract
This paper develops simple LMI-based criteria of controllability and observability for a linear time-invariant descriptor (differential-algebraic) multiple-input multiple-output (MIMO) system. Several examples illustrate the efficiency of the developed criteria. A restriction of these criteria is that the number of inputs (outputs, respectively) must not be smaller than half the states of the space dimension.
Similar content being viewed by others
References
Handbook on the Theory of Automatic Control, Ed. by A. A. Krasovskii (Nauka, Moscow, 1987) [in Russian].
Machine Building, Encyclopedy, Vol. 1–4: Automatic Control. The Theory (Mashinostroenie, Moscow, 2000) [in Russian].
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Halsted, New York, 1977; Nauka, Moscow, 1977).
G. H. Golub and Ch. F. van Loan, Matrix Computations, Johns Hopkins Studies in Mathematical Sciences (Johns Hopkins Univ. Press, Baltimore, USA, 1996).
L. Dai, Singular Control Systems (Springer, Berlin, 1989).
M. Sh. Misrikhanov and V. N. Ryabchenko, “Band criteria and recursive tests of complete controllability and observability of linear algebraic-differentiable systems,” Autom. Remote Control 69, 1486 (2008).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Finite Eigenvalue assignment for a descriptor system,” Dokl. Math. 91, 64 (2015).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Output control of the spectrum of a descriptor dynamical system,” Dokl. Math. 93, 259 (2016).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Spacecraft attitude control with simultaneous unloading of the angular momentum of inertial actuators,” J. Comput. Syst. Sci. Int. 54, 621 (2015).
O. M. Budargin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “The new criteria of large dynamic system controlability and observability,” Probl. Upravl., No. 1, 21–25 (2012).
J. W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, 1997).
M. Sh. Misrikhanov and V. N. Ryabchenko, “Algebraic and matrix methods in the theory of linear MIMO-systems,” Vest. IGEU, No. 5, 196–240 (2005).
R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design (Taylor and Francis, London, 1998).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zubov, N.E., Mikrin, E.A., Misrikhanov, M.S. et al. LMI-Based Criteria of Controllability and Observability for a Descriptor MIMO System. J. Comput. Syst. Sci. Int. 57, 18–24 (2018). https://doi.org/10.1134/S1064230718010148
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230718010148