Mean square exponential stability

Vasile Drăgan (), Toader Morozan () and Adrian-Mihail Stoica
Additional contact information
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

Chapter 3 in Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems, 2010, pp 59-101 from Springer

Abstract: 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.

Keywords: State Equilibrium; Markov Chain; Exponential Stability; Converse Implication; Periodic Case (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-0630-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9781441906304

DOI: 10.1007/978-1-4419-0630-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().