Abstract
Continuous-time processes that can be modeled by linear differential equations with constant coefficients can also be described in a systematic way in terms of state variable descriptions of the form \(\dot{x}(t) = Ax(t) + Bu(t),\ y(t) = Cx(t) + Du(t)\). The response of such systems due to a given input and a set of initial conditions is derived and expressed in terms of the variation of constants formula. Equivalence of state variable descriptions is also discussed.
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© 2014 Springer-Verlag London
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Antsaklis, P.J. (2014). Linear Systems: Continuous-Time, Time-Invariant State Variable Descriptions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_186-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_186-1
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Publisher Name: Springer, London
Online ISBN: 978-1-4471-5102-9
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