Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Systems: Discrete-Time, Time-Varying, State Variable Descriptions

  • P. J. Antsaklis
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_191-1


Discrete-time processes that can be modeled by linear difference equations with time-varying coefficients can be written in terms of state variable descriptions of the form \(x(k + 1) = A(k)x(k) + B(k)u(k),\ y(k) = C(k)x(k) + D(k)u(k)\). The response of such systems due to a given input and initial conditions is derived. Equivalence of state variable descriptions is also discussed.


Linear systems Discrete-time Time-varying State variable descriptions 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

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