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Study on general stability and stabilizability of linear discrete‐time stochastic systems
Author(s) -
Hou Ting,
Zhang Weihai,
Chen BorSen
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.238
Subject(s) - stability (learning theory) , mathematics , linear matrix inequality , exponential stability , lyapunov exponent , moment (physics) , control theory (sociology) , state (computer science) , control (management) , computer science , mathematical optimization , nonlinear system , algorithm , physics , classical mechanics , quantum mechanics , machine learning , artificial intelligence
AbstractWith the aid of spectrum technique, a new concept called “ (0, α)‐stabilizability” (0<α≤1) is introduced, for which a necessary and sufficient condition is also proposed via a linear matrix inequality (LMI)‐based approach. Especially, (0, α)‐stabilizability is identical with asymptotic mean square stabilizability when α=1. A more general regional stability called “ R ‐stability” is discussed extensively and some concrete examples are given. As applications, the relationship among (0, α;β)‐stability, the decay rate of the system state response and the second‐order moment Lyapunov exponent is revealed.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society