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Structural Properties of Linear Stochastic Systems

In: Mathematical Methods in Robust Control of Linear Stochastic Systems

Author

Listed:
  • Vasile Dragan

    (Institute of Mathematics of the Romanian Academy)

  • Toader Morozan

    (Institute of Mathematics of the Romanian Academy)

  • Adrian-Mihail Stoica

    (University Politechnica of Bucharest)

Abstract

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

Suggested Citation

  • Vasile Dragan & Toader Morozan & Adrian-Mihail Stoica, 2013. "Structural Properties of Linear Stochastic Systems," Springer Books, in: Mathematical Methods in Robust Control of Linear Stochastic Systems, edition 2, chapter 0, pages 163-187, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8663-3_4
    DOI: 10.1007/978-1-4614-8663-3_4
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