Low-order control design for LMI problems using alternating projection methods

Automatica

Volumn 32, Issue 8, 1996, Pages 1117-1125

  Grigoriadis, Karolos M ^a   Skelton, Robert E ^b  

^a UNIVERSITY OF HOUSTON   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Alternating projection methods; Control systems design; H control, linear matrix inequalities; Iterative methods; Low order controllers; State space methods

Indexed keywords

CALCULATIONS; CONTROL EQUIPMENT; CONTROL SYSTEMS; ITERATIVE METHODS; MATRIX ALGEBRA;

CONTROL SYSTEMS DESIGN; LINEAR MATRIX INEQUALITIES; LOW-ORDER CONTROLLERS; STATE-SPACE METHODS;

COMPUTER AIDED DESIGN;

EID: 0030219267     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(96)00057-X     Document Type: Article

References (31)

1. Boyd, S. P. and G. H. Barratt (1991). Linear Controller Design: Limits of Performance, Prentice-Hall, Englewood Cliffs, NJ.
2. Boyd, S. and L. El Ghaoui (1993). Methods of centers for minimizing generalized eigenvalues. Lin. Algebra Applics. 188/189, 63-111.
3. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Applied Mathematics, Philadelphia.
4. Boyle, J. P. and R. L. Dysktra (1986). A method for finding projections onto the intersection of convex sets in Hilbert space. In Advances in Order Restricted Statistical Inference, pp. 28-43. Lecture Notes in Statistics, Vol. 37. Springer-Verlag, Berlin.
5. Cheney, W. and A. A. Goldstein (1959). Proximity maps for convex sets. Proc. Am. Math. Soc., 12, 448-450.
6. Combettes, P. L. (1993). The foundations of set theoretic estimation. Proc. IEEE, 81, 182-208.
7. Combettes, P. L. and H. J. Trussell (1990). Method of successive projections for finding a common point of sets in metric spaces. J. Optim. Theory Applics, 67, 487-507.
8. David, J. and B. De Moor (1993). The opposite of analytic centering for solving minimum rank problems in control and identification. In Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, pp. 2901-2902.
9. El Ghaoui, L. and P. Gahinet (1993). Rank minimization under LMI constraints: a framework for output feedback problems. In Proc. European Control. Conf., Groningen, pp. 1176-1179.
10. ∞ suboptimal controllers. In Proc. 1992 American Control Conf., Chicago, IL, pp. 2240-2244.
11. ∞ controllers with applications. In Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, pp. 656-661.
12. ∞ control. Int. J. Robust Nonlin. Control, 4, 421-448.
13. Gahinet, P. and N. Nemirovskii (1993). General-purpose LMI solvers with benchmarks. In Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, pp. 3162-3165.
14. Grigoriadis, K. M. and R. E. Skelton (1992). Alternating convex projection methods for covariance control design. In Proc. 30th Allerton Conf. on Communication, Control and Computing, Urbana-Champaign, IL, pp. 88-97. Also Int. J. Control, 60, 1083-1106 (1994).
15. Grigoriadis, K. M. and R. E. Skelton (1992). Alternating convex projection methods for covariance control design. In Proc. 30th Allerton Conf. on Communication, Control and Computing, Urbana-Champaign, IL, pp. 88-97. Also Int. J. Control, 60, 1083-1106 (1994).
16. Grigoriadis, K. M. and R. E. Skelton (1993). Low-order control design for LMI problems using alternating projection methods. In Proc. 31st Allerton Conf. on Communication, Control and Computing, Urbana-Champaign, IL, pp. 231-240.
17. Grigoriadis, K. M., R. E. Skelton and A. E. Frazho (1993). Alternating convex projection methods for discrete-time covariance control design. In Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, pp. 1782-1786.
18. Gubin, L. G., B. T. Polyak and E. V. Raik (1967). The method of projections for finding the common point of convex sets. USSR Comp. Math. Phys., 7, 1-24.
19. Han, S. P. (1988). A successive projection method. Math. Program., 40, 1-14.
20. Higham, N. J. (1988). Computing the nearest symmetric positive semidefinite matrix. Lin. Algebra Applics, 103, 103-118.
21. Horn, R. A. and C. R. Johnson (1985). Matrix Analysis. Cambridge University Press.
22. ∞ control design problem: LMI existence conditions and state space formulas. Automatica, 30, 1307-1317.
23. Iwasaki, T. and R. E. Skelton (1995). Parametrization of all stabilizing controllers via quadratic Lyapunov functions. J. Optim. Theory Applics, 83, 291-307.
24. Luenberger, D. G. (1968). Optimization by Vector Space Methods. Wiley, New York.
25. Nesterov, Y. and A. Nemirovskii (1994). Interior-point polynomial algorithms in Convex Programming. SIAM Studies in Applied Mathematics, Philadelphia.
26. Packard, A., K. Zhou, P. Pandey and G. Becker (1991). A collection of robust control problems leading to LMIs. In Proc. 30th IEEE Conf. on Decision and Control, Brighton, U.K., pp. 1245-1250.
27. Skelton. R. E., T. Iwasaki and K. M. Grigoriadis (1996). A Unified Algebraic Approach to Linear Control Design. Taylor & Francis, Basingstoke (to appear).
28. Potter, L. C. (1991). Convergence of successive approximations for nonexpansive operators. In Proc. 29th Allerton Conf. on Communication, Control and Computing, Urbana-Champaign, IL, pp. 149-158.
29. Vandenberghe, L. and S. Boyd (1995). Primal-dual potential reduction methods for problems involving matrix inequalities. Math. Program, 69, 205-236.
30. Weber, C. A. and Allebach, J. P. (1986). Reconstruction of frequency-offset Fourier data by alternating projection onto constraint sets. In Proc. 24th Allerton Conf. on Communication, Control and Computing, Urbana-Champaign, IL, pp. 194-201.
31. Youla, D. C. and H. Webb (1982). Image restoration by the method of convex projections: Part 1 - Theory. IEEE Trans. Medical Imag., 1, 81-94.