Abstract
Continuous-time processes that can be modeled by linear differential equations with time-varying coefficients can be written in terms of state variable descriptions of the form \(\dot{x}(t) = A(t)x(t) + B(t)u(t),\ y(t) = C(t)x(t) + D(t)u(t)\). The response of such systems due to a given input and initial conditions is derived using the Peano-Baker series. Equivalence of state variable descriptions is also discussed.
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Bibliography
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Antsaklis, P.J. (2014). Linear Systems: Continuous-Time, Time-Varying 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_190-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_190-1
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Publisher Name: Springer, London
Online ISBN: 978-1-4471-5102-9
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