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Published in:
Applications of Observability Inequalities Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Minimal Set of Generators of Controllability Space for Singular Linear Systems

Author : María Isabel García-Planas

Published in: Recent Advances in Differential Equations and Applications

Publisher: Springer International Publishing

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Abstract

In recent years, there has been increasing the interest in the descriptive analysis of singular (also called generalized) systems in the form \(E\dot x(t)=Ax(t)\) because they play important roles in mathematical modelling problems permeating many aspects of daily life arising in a wide range of applications. Considerable advances have been obtained in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the exact controllability measuring the minimum set of controls that are needed to steer the whole system \(E\dot x(t)=Ax(t)\) toward any desired state. In this paper, we focus the study on the obtention of the set of all B making the system \(E\dot x(t)=Ax(t)+Bu(t)\) controllable.

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previous chapter Linear Elimination in Chemical Reaction Networks
next chapter On Stability of Discontinuous Galerkin Approximations to Anisotropic Stokes Equations
Literature
1.
Assan, J., Lafay, A., Perdon, A.: Computation of maximal pre-controllability submodules over a Noetherian ring. Syst. Control Lett. 37, 153–161 (1999)MathSciNetCrossRef
2.
Berger, T., Ilchmann, A., Trenn, S.: The quasi-Weierstraß form for regular matrix pencils. Linear Algebra Appl. 436, 4052–4069 (2012)MathSciNetCrossRef
3.
4.
Chen, C.T.: Introduction to Linear System Theory. Holt, Rinehart and Winston Inc, New York (1970)
5.
6.
7.
García-Planas, M.I.: Generalized controllability subspaces for time-invariant singular linear systems. In: Proceedings of Physcon 2011, IPACS Electronic Library (2011)
8.
9.
García-Planas, M.I., Domínguez, J.L.: Alternative tests for functional and pointwise output-controllability of linear time-invariant systems. Syst. Control Lett. 62, 382–387 (2013)MathSciNetCrossRef
10.
García-Planas, M.I., Tarragona, S., Diaz, A.: Controllability of time-invariant singular linear systems. In: From Physics to Control through an Emergent View, pp. 112–117. World Scientific, Singapore (2010)
11.
Hautus, M.L.J.: Controllability and observability conditions of linear autonomous systems. Nederl. Akad. Wetensch. (Reprinted form Proc. Ser. A 72 and Indag. Math. 31) 443–448 (1969)
12.
Heniche, A., Kamwa, I.: Using measures of controllability and observability for input and output selection. In: Proceedings of the 2002 IEEE International Conference on Control Applications, vol. 2, pp. 1248–1251 (2002)
13.
Kalman, R.E., Falb, P.L., Arbib, M.R.: Topics in Mathematical Control Theory. McGraw-Hill, New York/Toronto, Ontario/London (1969)MATH
14.
Kundur, P.: Power System Stability and Control. McGraw-Hill, New York (1994)
15.
16.
Liu, Y., Slotine, J., Barabási, A.: Controllability of complex networks. Nature 473, 167–173 (2011)CrossRef
17.
Shields, R., Pearson, J.: Structural controllability of multi-input linear systems. IEEE Trans. Autom. Control 21, 203–212 (1976)CrossRef
18.
19.
Yuan, Z.Z., Zhao, C., Wang, W.X., Di, Z.R., Lai, Y.C.: Exact controllability of multiplex networks. New J. Phys. 16, 1–24 (2014)MathSciNet
Metadata
Title
Minimal Set of Generators of Controllability Space for Singular Linear Systems
Author
María Isabel García-Planas
Copyright Year
2019
Book
Recent Advances in Differential Equations and Applications

Print ISBN: 978-3-030-00340-1

Electronic ISBN: 978-3-030-00341-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-00341-8_12

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