- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 890925, 6 pages
On Uniqueness of Strong Solution of Stochastic Systems
School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 265590, China
Received 25 October 2013; Revised 5 January 2014; Accepted 11 January 2014; Published 24 February 2014
Academic Editor: Antonio Suárez
Copyright © 2014 Gang Li and Ming Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Z. Has'minskii, Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, Alphen, The Netherlands, 1980.
- H. J. Kushner, Stochastic Stability and Control, Academic Press, New York, NY, USA, 1967.
- M. A. Rami and X. Y. Zhou, “Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls,” IEEE Transactions on Automatic Control, vol. 45, no. 6, pp. 1131–1143, 2000.
- T. Damm, Rational Matrix Equations in Stochastic Control, vol. 287 of Lecture Notes in Control and Information Sciences, Springer, New York, NY, USA, 2004.
- X. Mao, Stochastic Differential Equations and Their Applications, Horwood, Chichester, UK, 1997.
- Y. Liu, Backward stochastic differential equation and stochastic control system [Ph.D. thesis], Shandong University, Jinan, China, 1999.
- S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
- M. D. Fragoso, O. L. V. Costa, and C. E. de Souza, “A new approach to linearly perturbed Riccati equations arising in stochastic control,” Applied Mathematics and Optimization, vol. 37, no. 1, pp. 99–126, 1998.
- W. H. Zhang, H. S. Zhang, and B.-S. Chen, “Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1630–1642, 2008.
- W. H. Zhang and B.-S. Chen, “On stabilizability and exact observability of stochastic systems with their applications,” Automatica, vol. 40, no. 1, pp. 87–94, 2004.
- W. Zhang and B.-S. Chen, “Some properties of generalized Lyapunov equations,” in Proceedings of the Chinese Control and Decision Conference (CCDC '11), pp. 3137–3141, Mianyang, China, May 2011.
- S. B. Nadler, Continuum Theory: An Introduction, Marcel Dekker, New York, NY, USA, 1992.
- A. G. Mazko, “The Lyapunov matrix equation for a certain class of regions bounded by algebraic curves,” Soviet Automatic Control, vol. 42, pp. 12–17, 1980.
- W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM Journal on Control and Optimization, vol. 6, pp. 681–697, 1968.
- J. M. Ortega, Matrix Theory, Plenum Press, New York, NY, USA, 1987.
- V. M. Ungureanu and V. Dragan, “Nonlinear differential equations of Riccati type on ordered Banach spaces,” Electronic Journal of Qualitative Theory of Differential Equations, no. 17, pp. 1–22, 2012.