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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Antsaklis PJ, Michel AN (2006) Linear systems. Birkhauser, Boston
Brockett RW (1970) Finite dimensional linear systems. Wiley, New York
Chen CT (1984) Linear system theory and design. Holt, Rinehart and Winston, New York
DeCarlo RA (1989) Linear systems. Prentice-Hall, Englewood Cliffs
Hespanha JP (2009) Linear systems theory. Princeton Press, Princeton
Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs
Rugh WJ (1996) Linear systems theory, 2nd edn. Prentice-Hall, Englewood Cliffs
Sontag ED (1990) Mathematical control theory: deterministic finite dimensional systems. Texts in applied mathematics, vol 6. Springer, New York
Zadeh LA, Desoer CA (1963) Linear system theory: the state space approach. McGraw-Hill, New York
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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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