On two discrete-time system stability concepts and supermartingales
dc.contributor.author | Beutler, Frederick J. (Frederick Joseph) | en_US |
dc.date.accessioned | 2006-04-17T16:34:15Z | |
dc.date.available | 2006-04-17T16:34:15Z | |
dc.date.issued | 1973-11 | en_US |
dc.identifier.citation | Beutler, Frederick J. (1973/11)."On two discrete-time system stability concepts and supermartingales." Journal of Mathematical Analysis and Applications 44(2): 464-471. <http://hdl.handle.net/2027.42/33783> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6WK2-4CRHYN9-B7/2/b4828b4a76359a98e1972d88e31f2999 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/33783 | |
dc.description.abstract | A random discrete-time system {xn}, N = 0, 1, 2, ... is called stochastically stable if for every [epsilon] > 0 there exists a [lambda] > 0 such that the probability P[(supn || xn ||) > [epsilon]] P[|| x0 || > [lambda]] V([middle dot]) satisfies the supermartingale definition on {V(xn)} in a neighborhood of the origin; earlier proofs of stochastic stability require additional restrictions. A criterion for xn --> 0 almost surely is developed. It consists of a global inequality on {U(xn)} stronger than the supermartingale defining inequality, but applied to a U([middle dot]) that need not be a Lyapunov function. The existence of such a U([middle dot]) is exhibited for a stochastically unstable nontrivial stochastic system. This indicates that our criterion for xn --> 0 is "tight," and that the two stability concepts studied are substantially distinct. | en_US |
dc.format.extent | 467590 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | On two discrete-time system stability concepts and supermartingales | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Computer, Information & Control Engineering Program, University of Michigan, Ann Arbor, Michigan 48104, U.S.A. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/33783/1/0000037.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0022-247X(73)90071-1 | en_US |
dc.identifier.source | Journal of Mathematical Analysis and Applications | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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