Abstract
Consider a linear system whose parameters are disturbed by white noise:
(Ito stochastic differential equation). Here A,A 1 ∈ ℝn×n and w 1 is a standard real-valued Wiener process on a probability space (Ω,F,µ) relative to an increasing family (F t )t∈ℝ+ of σ-algebras F t ⊂ F. For every x 0 ∈ℝn there exists a unique solution x(t) = x(t,x 0) of (26.1) on ℝ+ = [0,∞) with x(0) = x 0.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Arnold. Stochastic Differential Equations: Theory and Applications. J. Wiley, New York, 1974.
A. El Bouhtouri and A. J. Pritchard. Stability radii of linear systems with respect to stochastic perturbations. Systems & Control Letters 19: 29–33, 1992.
R. Z. Has’minskii. Stochastic stability of differential equations. Sijthoff & Noordhoff, Alphen aan den Rijn, 1980 (translation of the Russian edition, Moscow, Nauka 1969 ).
D. Hinrichsen and A. J. Pritchard. Stability margins for systems with deterministic and stochastic uncertainty. Proc. 33rd IEEE Conf. Decision and Control, Florida 1994.
D. Hinrichsen and A. J. Pritchard. Stability radii of systems with stochastic uncertainty and their optimization by output feedback. SIAM J. Control and Optimization 34: 1972–1998, 1996.
D. Hinrichsen and A. J. Pritchard. Stochastic H ∞. IDS-Report 336, University of Bremen, 1996, accepted for publication in SIAM J. Control and Optimization.
T. Morozan. Stability radii for some stochastic differential equations. Stochastics and Stochastics Reports 54: 281–291, 1995.
J. L. Willems and J. C. Willems. Robust stabilization of uncertain systems. SIAM J. Control and Optimization 21: 352–374, 1983.
W. M. Wonham. Optimal stationary control of a linear system with state dependent noise. SIAM J. Control and Optimization 5: 486–500, 1967.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag London Limited
About this chapter
Cite this chapter
Hinrichsen, D., Pritchard, A.J. (1999). Robust stability of linear stochastic systems. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_26
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0807-8_26
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1207-5
Online ISBN: 978-1-4471-0807-8
eBook Packages: Springer Book Archive