On the rank minimization problem and its control applications

Systems and Control Letters

Volumn 33, Issue 1, 1998, Pages 31-36

  Mesbahi, Mehran ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Rank minimization under LMI constraints; Reduced order output feedback synthesis; Semi definite programming

Indexed keywords

EID: 0002325164     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(97)00111-4     Document Type: Article

References (11)

1. W.N. Anderson, Jr., Series and parallel addition of matrices, J. Math. Anal. Appl. 26 (3) (1969) 576-594.
2. T. Ando, private communication (1996).
3. D.S. Bernstein, Some open problems in matrix theory arising in linear systems and control, Linear Algebra Appl. 162-164 (1992) 409-432.
4. V. Blondel, M. Gevers, A. Lindquist, Survey on the state of systems and control, European J. Control 1 (1995) 5-23.
5. S.P. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
6. L. El Ghaoui, P. Gahinet, Rank minimization under LMI constraints: a framework for output feedback problems, in: Proc. European Control Conf., 1993.
7. K.M. Grigoriadis, R.E. Skelton, Fixed-order control design for LMI control problems using alternating projection method, in: Proc. IEEE Conf. Decision and Control, 1994.
8. R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge, 1985.
9. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge, 1991.
10. ∞ control problem: LMI existence conditions and state space formulas, in: Proc. American Control Conf., 1993.
11. M. Mesbahi, G.P. Papavassilopoulos, On the rank minimization problem over a positive semi-definite linear matrix inequality, IEEE Trans. Automat. Control 42 (2) (1997) 239-243.