Abstract
In this chapter basic information about linear differential equations are recalled and the main concepts of control theory, controllability and observability, are studied. Specific formulae for controls transferring one state onto another as well as algebraic characterizations of controllable and observable systems are obtained. A complete classification of controllable systems with one-dimensional input is given.
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Basic concepts of the chapter are due to R. Kalman [55]. He is also the author of Theorems 1.2, 1.5, 1.6 and 1.7. Exercise 1.3 as well as Proposition 1.3 are due to R. Triggiani [94]. A generalization of Theorem 1.4 to arbitrary m leads to the so-called controllability indices discussed in W.A. Wolvich [99], W.M. Wonham [101], R.W. Brockett [12].
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Zabczyk, J. (2020). Controllability and observability. In: Mathematical Control Theory. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44778-6_1
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DOI: https://doi.org/10.1007/978-3-030-44778-6_1
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-44776-2
Online ISBN: 978-3-030-44778-6
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