Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Systems: Continuous-Time, Time-Invariant State Variable Descriptions

  • Panos J. AntsaklisEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_186-1


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.


Linear systems Continuous-time Time-invariant State variable descriptions 
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© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA