Abstract
Starting with Newtonian dynamics, the natural evolution processes have been described by differential equations. Much later, technological development allowed consideration of systems whose motion is no longer determined only by natural laws but also is influenced by controls. The first such controller seems to be the one of Watt. From a mathematical viewpoint the control devices are described by functions that modify the system of differential equations in order to obtain desired properties of the evolution.
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Notes and References
There are many books devoted to the general theory of control systems including the stabilization problem. Some of the most popular are the ones by H. Kwakernak and R. Sivan [44], E. D. Sontag [59], W. M. Wonham [63], and J. Zabczyk [68].
For stability theory of linear systems, important references are the books of T. Chen [4], T. Kailath [31], and W. J. Rugh [53]. For nonlinear systems stability theory and Liapunov functions, we also refer to the books of W. Hahn [21], A. Halanay and V. Răsvan [23], and H. K. Khalil [37].
For general theory of differential equation, important references are the books of J. K. Hale [25] and R. K. Miller and A. N. Michel [49]. We may also refer to the book of A. Halanay [22].
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© 1999 Springer Science+Business Media New York
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Dragan, V., Halanay, A. (1999). Introduction. In: Stabilization of Linear Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1570-7_1
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DOI: https://doi.org/10.1007/978-1-4612-1570-7_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7197-0
Online ISBN: 978-1-4612-1570-7
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