Structural Properties of Linear Stochastic Systems

  • Vasile Dragan
  • Toader Morozan
  • Adrian-Mihail Stoica


In this chapter we present the stochastic version of some basic concepts in control theory, namely the stabilizability, detectability, observability and controllability. All these concepts are defined both in Lyapunov operators terms and in stochastic systems terms. The definitions given in this chapter extend the corresponding definitions from the deterministic time-varying systems. Some examples will show that the stochastic observability does not always imply stochastic detectability and stochastic controllability does not necessarily imply stochastic stabilizability. As in the deterministic case the concepts of stochastic detectability and observability are used in some criteria of exponential stability in mean square


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Vasile Dragan
    • 1
  • Toader Morozan
    • 1
  • Adrian-Mihail Stoica
    • 2
  1. 1.Institute of Mathematics of the Romanian AcademyBucharestRomania
  2. 2.University Politechnica of BucharestBucharestRomania

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