Quadratic stabilization and control of piecewise-linear systems

Proceedings of the American Control Conference

Volumn 6, Issue , 1998, Pages 3659-3664

  Hassibi, Arash ^a   Boyd, Stephen ^a  

^a Stanford University   (United States)

Author keywords

Linear matrix inequality (LMI); Piecewise linear systems; Quadratic stabilization

Indexed keywords

CONTROLLER SYNTHESIS; CONVEX OPTIMIZATION PROBLEMS; PIECE-WISE LINEAR SYSTEMS; QUADRATIC STABILIZATION;

CONVEX OPTIMIZATION; FEEDBACK; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; STABILIZATION;

PIECEWISE LINEAR TECHNIQUES;

EID: 84881361335     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.1998.703296     Document Type: Conference Paper

References (17)

1. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, Volume 15 of Studies in Applied Mathematics. SIAM, Philadelphia, PA, June 1994.
2. G. Becker, A. Packard, D. Philbrick, and G. Balas. Control of parametrically dependent linear systems: a single quadratic Lyapunov approach. In 1993 American Control Conference, Volume 3, pages 2795-2799, June 1993.
3. ∞ controllers. IEEE Transactions on Automatic Control, 40(5):853-864, May 1995.
4. R. E. Skelton, T. Iwasaki, and K. Grigoriadis. A Unified Algebraic Approach to Linear Control Design. Taylor and Francis, 1998.
5. A. Megretski. Synthesis of robust controllers for systems with integral and quadratic constraints. In Proc. IEEE Conf. on Decision and Control, Volume 3, pages 3092-3097, New York, NY, 1994.
6. ∞ analysis and control of linear systems with integral quadratic constraints. In Proc. of the European Contr. Conf, Volume 1, pages 195-200, July 1995.
7. ∞ control theory, and linear matrix inequalities. IEEE Trans, on Fuzzy Systems, 4(1):1-13, February 1996.
8. J. Zhao, V. Wertz, and R. H. Gorez. Design a stabilizing fuzzy and/or non-fuzzy state-feedback controller using LMI method. Proc. European Control Conf., 2:1201-1206, September 1995.
9. M. Johansson and Anders Rantzer. Computation of piece-wise quadratic lyapunov functions for hybrid systems. Technical Report ISRN LUTFD2/TFRT-7549-SE, Dept. of Automatic Control, Lund Institute of Technology, June 1996.
10. A. Rantzer and M. Johansson. Piecewise quadratic optimal control. In Proc. American Control Conf, 1997.
11. L. Vandenberghe, S. Boyd, and S.-P. Wu. Determinant maximization with linear matrix inequality constraints. SIAM J. on Matrix Analysis and Applications, April 1998. To appear.
12. Yu. Nesterov and A. Nemirovsky. Interior-point polynomial methods in convex programming, Volume 13 of Studies in Applied Mathematics. SIAM, Philadelphia, PA, 1994.
13. F. P. Preparata and M. I. Shamos. Computational Geometry, an Introduction. Texts and monographs in Computer Science. Springer-Verlag, New York, 1985.
14. S.-P. Wu and S. Boyd. SDPSOL: A Parser/Solver for Semidefinite Programming and Determinant Maximization Problems with Matrix Structure. User's Guide, Version Beta. Stanford University, June 1996.
15. P. P. Varaiya. Smart cars on smart roads: Problems of control. IEEE Trans. Aut. Control, 38(2):195-207, 1993.
16. A. Göllü and P. Varaiya. Hybrid dynamical systems. In Proc. IEEE Conf. on Decision and Control, pages 2708-2712, Tampa, Florida, December 1989.
17. R. W. Brockett. Hybrid models for motion control systems. In H. L. Trentelman and J. C. Willems, editors, Essays in Control: Perspectives in the Theory and its Applications, pages 29-53. Birkhauser, Boston, 1993.