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Mean square exponential stability

In: Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems

Author

Listed:
  • Vasile Drăgan

    (Institute of Mathematics “Simion Stoilow” of the Romanian Academy)

  • Toader Morozan

    (Institute of Mathematics “Simion Stoilow” of the Romanian Academy)

  • Adrian-Mihail Stoica

    (University “Politehnica” of Bucharest, Faculty of Aerospace Engineering)

Abstract

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.

Suggested Citation

  • Vasile Drăgan & Toader Morozan & Adrian-Mihail Stoica, 2010. "Mean square exponential stability," Springer Books, in: Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems, edition 0, chapter 3, pages 59-101, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0630-4_3
    DOI: 10.1007/978-1-4419-0630-4_3
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