Discrete-time state representations, a new paradigm

  • S. Monaco
  • D. Normand-Cyrot

Summary

Continuing the study of discrete-time dynamical systems, a new state representation of discrete-time dynamics is proposed, whose development has been largely inspired by pioneering works of I. D. Landau. Breaking with the traditional idea of modelling discrete-time processes as difference equations we here propose to represent discrete-time dynamics as coupled difference and differential equations. The difference equation models, through jumps, the free evolution or a nominal one associated with some constant control value while the differential equation models the influence of the control. The differential structure is at the basis of a geometric study which enables us to stress some intriguing analogies with continuous-time, in particular regarding the control dependency of the dynamics compared to the time dependency. The present paper aims at convincing the reader that such a differential modelling might be the proper way to define and represent forced discrete-time behaviours. This would completely renew the understanding and the methodologies used when discussing discrete-time dynamics in modelling or control contexts.

Keywords

Manifold Lution Dipt 

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Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • S. Monaco
    • 1
  • D. Normand-Cyrot
    • 2
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Laboratoire des Signaux et SystèmesCNRS-ESEGif sur YvetteFrance

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