Abstract
The topic of this chapter is the structure at infinity of discrete and continuous linear time-varying systems in a unified approach. When interconnecting two subsystems, ”impulsive motions” may arise. In the continuous-time case, those impulsive motions are linear combinations of the Dirac distribution δ and its derivatives; they were first studied by Verghese [346]. In the discrete-time case, those impulsive behaviors are backward solutions with finite support; they were revealed by Lewis [216]. The space spanned by all impulsive motions of a system is called its ”impulsive behavior” and is denoted as \( \mathfrak{B}_{\infty }\). The structure of this impulsive behavior must be studied, and, for the integrity of the system resulting from the interconnection, all impulsive motions must be avoided.
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© 2011 Springer-Verlag Berlin Heidelberg
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Bourlès, H., Marinescu, B. (2011). Structure at Infinity and Impulsive Behaviors. In: Linear Time-Varying Systems. Lecture Notes in Control and Information Sciences, vol 410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19727-7_7
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DOI: https://doi.org/10.1007/978-3-642-19727-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19726-0
Online ISBN: 978-3-642-19727-7
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