Analysis of linear systems with saturation using convex optimization

Proceedings of the IEEE Conference on Decision and Control

Volumn 1, Issue , 1998, Pages 903-908

  Hindi, Haitham ^a   Boyd, Stephen ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCLE CRITERIA; CONVEX OPTIMIZATION; LINEAR MATRIX INEQUALITIES (LMI); POPOV CRITERIA; SATURATING ELEMENTS;

CONTROL SYSTEM ANALYSIS; FUNCTIONS; LYAPUNOV METHODS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; STATE SPACE METHODS; SYSTEM STABILITY;

LINEAR CONTROL SYSTEMS;

EID: 0032280895     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (18)

1. F. Blanchini and S. Miani. Constrained stabilization of continuous-time linear systems. Syst. Control Letters, 28:95-102, 1996.
2. S. Boyd and C Barratt. Linear Controller Design: Limits of Performance. Prentice-Hall, 1991.
3. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakr-ishnan. Linear Matrix Inequalities in System and Control Theory, volume 15 of Studies in Applied Mathematics. SIAM, Philadelphia, PA, June 1994.
4. E. J. Davison and E. M. Kurak. A computational method for determining quadratic Lyapunov functions for non-linear systems. Automatica, 7:627-636, 1971.
5. E. G. Gilbert and K. T. Tan. Linear systems with state and control constraints: Theory and application of maximal output admissible sets, IEEE Trans, Aut. Control, 36(9):1008-1019, September 1991.
6. A. H. Glattfelder and W. Schaufelberger. Stability analysis of single loop control systems with saturation and antireset-windup circuits. IEEE Trans. Aut. Control, AC-28(12):1074-1081, December 1983.
7. P. Gutman and M. Cwikel. An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states. IEEE Trans. Aut. Control, AC-32(3):251-254, March 1987.
8. H. Khalil. Nonlinear Systems. Macmillan, New York, NY, 1992.
9. R. L. Kosut. Design of linear systems with saturating linear control and bounded states. IEEE Trans. Aut. Control, AC-28(1):121-124, January 1983.
10. D, G. Luenberger. Linear and Nonlinear Programming. Addison-Wesley, Reading, Mass., 2nd edition, 1984.
11. T. Pare, J, How, H. Hindi, and S. Boyd. Synthesizing stability regions for systems with saturating actuators. Proc. IEEE Conf, on Decision and Control, December 1998.
12. C. Pittet, S. Tarboureich, and C. Burgat. Stability regions for linear systems with saturating controls via circle and Popov criteria. December 1997.
13. B. G. Romanchuk. Computing regions fo attraction with polytopes: Planar case. Automatica, 32(12):1727-1732, 1996
14. R. Skelton, T. Iwasaki, and K. Grigoriadis. A Unified Algebraic Approach to Linear Control Design. Taylor and Francis, Pennsylvania, 1998.
15. L. Vandenberghe, S. Boyd, and S.-P. Wu. Determinant maximization with linear matrix mequality constraints. SIAM J. on Matrix Analysis and Applications, 1996. to appear.
16. A. Vanelli and M, Vidyasagar. Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems. Automatica, 21(1):69-80, 1985.
17. J. A. Walker and N. H, McClamroch. Finite regions of attraction for the problem of Lur'e. Int. J, Control, 6(4):331-336, 1967.
18. S. Weisseuberger. Application of results from the absolute stability to the computation of finite stability domains. IEEE Trans. Aut. Control, AC-13:124-125, February 1968.