Abstract
An important input-output description of a linear discrete-time system is its (discrete-time) impulse response (or pulse response), which is the response h(k, k0) to a discrete impulse applied at time k0. In time-invariant systems that are also causal and at rest at time zero, the impulse response is h(k, 0), and its z-transform is the transfer function of the system. Expressions for h(k, k0) when the system is described by state variable equations are derived.
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Bibliography
Antsaklis PJ, Michel AN (2006) Linear systems. Birkhauser, Boston
Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs
Rugh WJ (1996) Linear systems theory, 2nd edn. Prentice-Hall, Englewood Cliffs
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© 2015 Springer-Verlag London
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Antsaklis, P.J. (2015). Linear Systems: Discrete-Time Impulse Response Descriptions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_189
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DOI: https://doi.org/10.1007/978-1-4471-5058-9_189
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Publisher Name: Springer, London
Print ISBN: 978-1-4471-5057-2
Online ISBN: 978-1-4471-5058-9
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