Mean square exponential stability

  • Vasile DrăganEmail author
  • Toader Morozan
  • Adrian-Mihail Stoica


The problem of mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. Four different definitions of the concept of exponential stability in the mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other three definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.


State Equilibrium Markov Chain Exponential Stability Converse Implication Periodic Case 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vasile Drăgan
    • 1
    Email author
  • 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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