Title :
Structured stochastic uncertainty
Author_Institution :
Dept. of Mech. Eng., Univ. of California at Santa Barbara, Santa Barbara, CA, USA
Abstract :
We consider linear time invariant systems in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. We provide a purely input-output treatment of these systems without recourse to state space models, and thus our results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for mean square stability in terms of the spectral radius of a linear matrix operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties.
Keywords :
discrete time systems; feedback; linear matrix inequalities; linear systems; stability; state-space methods; stochastic processes; additive noise; correlated uncertainties; distributed systems; feedback; input-output treatment; linear matrix operator; linear time invariant systems; mean square stability; multiplicative noise; necessary and sufficient conditions; state space model; structured stochastic uncertainty; uncorrelated uncertainties; Correlation; Covariance matrices; Stability analysis; Standards; Stochastic processes; Uncertainty; Vectors;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4673-4537-8
DOI :
10.1109/Allerton.2012.6483396
