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Structural properties of linear stochastic systems

  • Vasile Drăgan
  • Toader Morozan
  • Adrian-Mihail Stoica
Chapter

Abstract

In this chapter we present the stochastic version of some basic concepts in control theory, namely stabilizability, detectability, and observability. All these concepts are defined both in Lyapunov operator terms and in stochastic system terms. The definitions given in this chapter extend the corresponding definitions from the deterministic time-varying systems. Some examples show that 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 the mean square.

Keywords

Exponential Stability Stable Evolution Converse Implication Stochastic Matrix Stochastic Stabilizability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vasile Drăgan
    • 1
  • Toader Morozan
    • 1
  • Adrian-Mihail Stoica
    • 2
  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucuresti 1Romania
  2. 2.Faculty of Aerospace EngineeringUniversity “Politehnica” of BucharestBucurestiRomania

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