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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Antsaklis PJ, Michel AN (2006) Linear systems. Birkhauser, Boston
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Rugh WJ (1996) Linear systems theory, 2nd edn. Prentice-Hall, Englewood Cliffs
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Antsaklis, P.J. (2021). Linear Systems: Discrete-Time Impulse Response Descriptions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_189
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DOI: https://doi.org/10.1007/978-3-030-44184-5_189
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44183-8
Online ISBN: 978-3-030-44184-5
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