Non-smooth techniques for stabilizing linear systems

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 1245-1250

  Bompart, Vincent ^a   Apkarian, Pierre ^a   Noll, Dominikus ^b  

^a ONERA   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; SCHRODINGER EQUATION;

CLOSED-LOOP STABILIZATION; CONTROLLER SYNTHESIS; LINEAR TIME INVARIANT (LTI);

CLOSED LOOP SYSTEMS;

EID: 34548088882     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282408     Document Type: Conference Paper

References (24)

1. J. V. Burke, A. S. Lewis, and M. L. Overton, "Two numerical methods for optimizing matrix stability," Linear Algebra and its Applications, vol. 351-352, pp. 117-145, 2002.
2. V. Blondel and J. Tsitsiklis, "NP-hardness of some linear control design problems," SIAM Journal on Control and Optimization, vol. 35, no. 6, pp. 2118-2127, 1997.
3. D. S. Bernstein, "Some open problems in matrix theory arising in linear systems and control," Linear Algebra and its Applications, vol. 162-164, pp. 409-432, 1992.
4. J. V. Burke, A. S. Lewis, and M. L. Overton, "Optimizing matrix stability," Proceedings of the American Mathematical Society, vol. 129, pp. 1635-1642, 2001.
5. ∞ synthesis," IEEE Transactions on Automatic Control, vol. 51, no. 1, pp. 71-86, 2006.
6. _, "Nonsmooth optimization for multiband frequency domain control design," Automatica, vol. In Press, Corrected Proof, 2006.
7. ∞ synthesis," European Journal of Control, vol. 12, no. 3, pp. 229-244, 2006.
8. ∞ synthesis," in 5th IFAC Symposium on Robust Control Design, Toulouse, France, July 2006.
9. J. V. Burke and M. L. Overton, "Variational analysis of non-Lipschitz spectral functions," Mathematical Programming, vol. 90, no. 2, pp. 317-351, 2001.
10. _, "Differential properties of the spectral abscissa and the spectral radius for analytic matrix-valued mappings," Nonlinear Analysis: Theory, Methods & Applications, vol. 23, pp. 467-488, 1994.
11. J. B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms II. Springer-Verlag, 1993.
12. K. C. Kiwiel, Methods ofDescent for Nondifferentiable Optimization, ser. Lecture Notes in Mathematics 1133. Springer-Verlag, 1985, vol. 1133.
13. J. V. Burke, A. S. Lewis, and M. L. Overton, "Approximating subdifferentials by random sampling of gradients," Mathematics of Operations Research, vol. 27, pp. 567-584, 2002.
14. _, "A robust gradient sampling algorithm for nonsmooth, nonconvex optimization," SIAM Journal on Optimization, vol. 15, pp. 751-779, 2005.
15. R. J. Ober, "Balanced parametrizations of classes of linear systems," SIAM Journal on Control and Optimization, vol. 29, pp. 1251-1287, 1991.
16. F. H. Clarke, Optimization and Nonsmooth Analysis, ser. Canadian Math. Soc. Series. New York: John Wiley & Sons, 1983.
17. E. Polak, "On the mathematical foundations of nondifferentiable optimization in engineering design," SIAM Review, vol. 29, no. 1, pp. 21-89, 1987.
18. _, Optimization: Algorithms and Consistent Approximations. Springer-Verlag, 1997.
19. ∞ optimization," in 5th IFAC Symposium on Robust Control Design, Toulouse, France, July 2006.
20. V. Torczon, "Multi-directional search: A direct search algorithm for parallel machines," Ph.D. dissertation, Department of Mathematical Sciences, Rice University, Houston, Texas, May 1989.
21. _, "On the convergence of the multidirectional search algorithm," SIAM Journal on Optimization, vol. 1, no. 1, pp. 123-145, 1991.
22. P. Apkarian and D. Noll, "Controller design via nonsmooth multi-directional search," SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 1923-1949, 2006.
23. Optimization Toolbox User's Guide, The MathWorks, march 2006, version 3.
24. eib 1.0," University of Trier, Tech. Rep., 2003.