AUTHORS: Maria Isabel Garcia-Planas

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ABSTRACT: Due to the significant role played by singular systems in the form Ex˙(t) = Ax(t), on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact controllability by measuring the minimum set of controls needed to direct the entire system Ex˙(t) = Ax(t) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system Ex˙(t) = Ax(t) + Bu(t) controllable.

KEYWORDS: Controllability, exact controllability, eigenvalues, eigenvectors, singular linear systems

REFERENCES:

[1] G. Antoniou, Second-order Generalized Systems: The DFT Algorithm for Computing the Transfer Function, WSEAS Transactions on Circuits. 2002, pp. 151–153.

[2] J. Assan, A. Lafay and A. Perdon, Computation of maximal pre-controllability submodules over a Noetherian ring, Systems & Control Letters. 37(3), 1999, pp. 153–161.

[3] T. Berger, A. Ilchmann and S. Trenn, The quasiWeierstraß form for regular matrix pencils, Linear Algebra and its Applications. 436, 2012, pp. 4052–4069.

[4] F. Cardetti and M. Gordina, A note on local controllability on lie groups, Systems & Control Letters. 57, 2008, pp. 978–979.

[5] C.T. Chen, Introduction to Linear System Theory, Holt, Rinehart and Winston Inc, New York 1970

[6] M.I. Garc´ıa-Planas, Generalized Controllability Subspcaes for Time-invariant Singular Linear Systems, IPACS Electronic Library, 2011.

[7] M.I. Garc´ıa-Planas, Exact Controllability of Linear Dynamical Systems: a Geometrical Approach, Applications of Mathematics. 1, 2017, pp. 37–47, DOI:10.21136/AM.2016.0427-15

[8] M.I. Garc´ıa-Planas, Analizing exact controllability of l-order linear ystems. WSEAS transactions on systems and control. 12, pp. 232–239.

[9] M.I. Garc´ıa-Planas, El M. Souidi and L.E. Um, Convolutional codes under linear systems point of view. Analysis of output-controllability. WSEAS transactions on mathematics. 11(4), 2012, pp. 324–333.

[10] M.I. Garcia-Planas, S. Tarragona and A. Diaz, Controllability of time-invariant singular linear systems From physics to control through an emergent view, World Scientific, 2010, pp. 112– 117.

[11] M.I. Garcia-Planas and J.L. Dom´ınguez, Alternative tests for functional and pointwise outputcontrollability of linear time-invariant systems, Systems & control letters, 62(5), 2013, pp. 382– 387.

[12] M. Gugat, Exact Controllability In: Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems. Springer-Briefs in Electrical and Computer Engineering. Birkhuser, Cham, 2015.

[13] A. Heniche and I. Kamwa, Using measures of controllability and observability for input and output selection, Proceedings of the 2002 IEEE International Conference on Control Applications, 2, 2002, pp. 1248–1251.

[14] P. Kundur, Power System Stability and Control, McGraw-Hill, New York, USA 1994.

[15] C. Lin, Structural controllability, IEEE Trans. Automat. Contr. 19, 1974, pp. 201–208.

[16] Y. Liu, J. Slotine and A. Barabasi, Controlla- ´ bility of complex networks, Nature, 473(7346), 2011, pp. 167–173.

[17] A.K. Nandakumaran, Exact controllability of Linear Wave Equations and Hilbert Uniqueness Method, Proceedings, Computational Mathematics, Narosa, 2005.

[18] S. Nie, X. Wang, B. Wang Effect of degree correlation on exact controllability of multiplex networks Physica A: Statistical Mechanics and its Applications, 436(15), 2015, pp. 98–102.

[19] M. Posfai, J. Gao, S.P. Cornelius, A.L. Barab ´ asi ´ and R.M. D’Souza, Controllability of multiplex, multi-time-scale networks, Physical Review E, 94(3), 2016.

[20] R. Shields and J. Pearson, Structural controllability of multi-input linear systems. IEEE Trans. Automat. Contr, 21, 1976, pp.203–212.

[21] Kai-Tak Wong, The eigenvalue problem λT x + Sx, J. Differential Equations. 16, 1974, pp.270– 280.

[22] W-X. Wang, X. Ni, Y-C Lai and C. Grebogi, Optimizing controllability of complex networks by minimum structural perturbations, Phys. Rev. E85, 026115, 2012, pp. 1–5.

[23] Z.Z. Yuan, C. Zhao, W.X. Wang, Z.R. Di and Y.C. Lai, Exact controllability of multiplex networks, New Journal of Physics. 16, 2014, pp. 1- 24.