On upper estimate of anisotropic norm of uncertain system with application to stochastic robust control

References

• Bernstein, D. A. , & Haddad, W. M. (1989a). LQG control with an H∞ performance constraint: A Riccati equation approach. IEEE Transactions on Automatic Control , AC-34 (3), 293–305.
   Web of Science ®Google Scholar
• Bernstein, D. A. , & Haddad, W. M. (1989b). Robust stability and performance analysis for linear dynamic systems. IEEE Transactions on Automatic Control , AC-34 (4), 751–758.
   Web of Science ®Google Scholar
• Boyd, S. P. , El Ghaoui, L. , Feron, E. , & Balakrishnan, V . (1994). Linear matrix inequalities in systems and control theory . Philadelphia, PA: SIAM.
   Google Scholar
• Diamond, P. , Vladimirov, I. G. , Kurdyukov, A. P. , & Semyonov, A. V. (2001). Anisotropy-based performance analysis of linear discrete time invariant control system. International Journal of Control , 74 , 28–42.
   Web of Science ®Google Scholar
• Feron, E. , Balakrishnan, V. , Boyd, S. , & El Ghaoui, L. (1992, June). Numerical methods for H2 related problems. In Proceedings of American Control Conference , (pp. 2921–2922). Chicago, IL: The Council.
   Google Scholar
• Feron, E. (1997). Analysis of robust H2 performance using multiplier theory. SIAM Journal of Control & Optimization , 35 (1), 160–177.
   Web of Science ®Google Scholar
• Kurdyukov, A. P. , & Maximov, E. A. (2004). Robust stability of linear discrete stationary systems with uncertainty bounded in the anisotropic norm. Automation & Remote Control , 65 (12), 1977–1990.
   Web of Science ®Google Scholar
• Kurdyukov, A. P. , & Maximov, E. A. (2006). Solution of the stochastic H∞ -optimization problem for discrete time linear systems under parametric uncertainty. Automation & Remote Control , 67 , 1283–1310.
   Web of Science ®Google Scholar
• Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in Matlab . Proceedings of CACSD conference. Taipei, Taiwan.
   Google Scholar
• Packard, A. , , & Doyle, J. C . (1987). Robust control with an H 2 performance objective. In Proceedings of American Control Conference , IEEE (pp. 1213–1218).
   Google Scholar
• Paganini, R. D. F. , & Doyle, J . (1994). Behavioral approach to robustness analysis. In Proceedings of American Control Conference , (pp. 2782–2786). Baltimore, MD: IEEE.
   Google Scholar
• Paganini, R. D. F. , & Feron, E. (2000). LMI methods for robust H2 analysis: A survey with comparisons. In L. El Ghaoui S.-I Niculescu (Eds.) Advances in linear matrix inequality methods in control , Philadelphia, PA: SIAM.
   Google Scholar
• Petersen, I. R. (1987). A stabilization algorithm for a class of uncertain linear systems. System & Control Letters , 8 , 351–357.
   Web of Science ®Google Scholar
• Petersen, I. R. , & McFarlane, D. C. (1992, June). Optimal guaranteed cost control of uncertain linear systems . Proceedings of American Control Conference. Chicago, IL.
   Google Scholar
• Petersen, I. R. , McFarlane, D. C. , & Rotea, M. A. (1993, July). Optimal guaranteed cost control of discrete time uncertain systems. In G.C. Goodwin R.J. Evans (Eds.) Proceedings of 12th IFAC world congress (pp. 407–410). Sidney.
   Google Scholar
• Poznyak, A. S. (2008, 2009). Advanced mathematical tools for automatic control engineers. Volumes 1,2: Deterministic techniques, stochastic techniques . Oxford, UK; Amsterdam, NL: Elsevier.
   Google Scholar
• Stoorvogel, A. A. (1993). The robust H2 problem: A worst case design. IEEE Transactions on Automatic Control , 38 , 1358–1370.
   Web of Science ®Google Scholar
• Tchaikovsky, M. M. , & Kurdyukov, A. P. (2011). Strict anisotropic norm bounded real lemma in terms of matrix inequalities. Doklady Mathematics , 84 (3), 895–898.
   Web of Science ®Google Scholar
• Vladimirov, I. G. , Diamond, P. , & Kloeden, P. (2006). Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems. Automation & Remote Control , 67 (8), 92–111.
   Web of Science ®Google Scholar
• Vladimirov, I. G. , Kurdjukov, A. P. , & Semyonov, A. V. (1995). Anisotropy of signals and entropy of linear stationary systems. Doklady Mathematics , 51 (3), 388–390.
   Google Scholar
• Vladimirov, I. G. , Kurdjukov, A. P. , & Semyonov, A. V . (1996a). On computing the anisotropic norm of linear discrete-time-invariant systems. In T. McAvoy A.J. Niemi M. Kummel (Eds.) 13th IFAC World Congress , June 30–July 5, 1996, (pp. 179–184). San Francisco, CA: Pergamon, Oxford, UK.
   Google Scholar
• Vladimirov, I. G. , Kurdjukov, A. P. , Semyonov, A. V . (1996b). State-space solution to anisotropy-based stochastic H∞ -optimization problem. In T. McAvoy A.J. Niemi M. Kummel (Eds.) 13th IFAC World Congress (pp. 427–432). San-Francisco, CA: Pergamon, Oxford, UK.
   Google Scholar