State-feedback control design for continuous-time piecewise linear systems: An LMI approach

Proceedings of the American Control Conference

Volumn , Issue , 2008, Pages 1104-1108

  Ding, Da Wei ^a,b   Yang, Guang Hong ^a,b  

^a NORTHEASTERN UNIVERSITY   (China)

^b KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

Author keywords

Linear matrix inequalities; Piecewise linear systems; Piecewise quadratic Lypaunov function; Reciprocal projection lemma

Indexed keywords

CONTINUOUS TIME SYSTEMS; CONTROL SYSTEM SYNTHESIS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; FEEDBACK; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; PIECEWISE LINEAR TECHNIQUES; PROJECTION SYSTEMS; STATE FEEDBACK; TELECOMMUNICATION NETWORKS; VIBRATIONS (MECHANICAL);

CONTINUOUS-TIME; EXTRA VARIABLES; LMI APPROACH; LYAPUNOV; PIECE-WISE LINEAR; PIECEWISE LINEAR SYSTEMS; PIECEWISE QUADRATIC LYAPUNOV FUNCTION; PIECEWISE QUADRATIC LYPAUNOV FUNCTION; RECIPROCAL PROJECTION LEMMA; STATE-FEEDBACK CONTROL;

CONTROL SYSTEMS;

EID: 52449134084     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2008.4586640     Document Type: Conference Paper

References (25)

1. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints". Automatica, vol. 35, 1999, pp 407-427.
2. B. D. Schutter and B. D. Moor, "The extended linear complementarity problem and the modeling and analysis of hybrid systems". In P. Antsaklis, W. Kohn, M. Lemmon, A. Nerode and S.Satry(Eds) Hybrid Systems Verification and Control: Lecture Notes in Computer Science, vol.1567, pp 70-85. (Springer-Verlag).
3. E. D. Sontag, "Nonlinear regulation: the piecewise linear approach", IEEE Trans. Automat. Contr.,Vol. 26, pp. 346-357, 1981.
4. M. Corless, "Robust stability analysis and controller design with quadratic Lyapunov functions", in Variable Structure and Lyapunov Control, A. S. I. Zinober, Ed., 1994, ch. 9, pp. 181-203. Lecture notes in Control and Information Sciences.
5. J. I. Imura and Van der Schaft, "Characterization of well-posedness of piecewise-linear systems", IEEE Trans. Automat. Contr., Vol. 45, pp. 1600-1619. 2000.
6. E. D. Sontag, "Nonlinear regulation: the piecewise linear approach", IEEE Trans. Automat. Contr.,Vol. 26, pp. 346-357, 1981.
7. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions of hybrid systems", IEEE Trans. Automat. Contr., Vol. 43, no.4, pp. 555-559, 1998.
8. A. Rantzer and M. Johansson, "Piecewise linear quadratic optimal control", IEEE Trans. Automat. Contr., Vol. 45, no.4, pp. 629-637, 2000.
9. M. Johansson, Piecewise Linear Control Systems, Springer-verlag, 2003.
10. G. Feng, "Stability analysis of piecewise discret-time linear systems", IEEE Trans. Automat. Contr., Vol. 47, no. 7, pp. 1108-1112, 2002.
11. A. Hassibi, and S. Boyd, "Quadratic stabilization and control of piecewise-linear systems", Proc. American Contol Confenrence, Philadephia, Pennsylvania, pp. 3659-3664, 1998.
12. L. Rodrigues and J. H. How, "Observer-based control of piecewise-affine systems", Int. J. Control., vol. 76, pp. 459-477, 2003.
13. L. Rodrigues and S. Boyd, "Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization", Systems and Control Letters, vol. 54, pp. 835-853, 2005.
14. G. Feng, "Controller design and analysis of uncertain piecewise-linear systems", IEEE Trans. Circuits. Syst. I, Vol. 49, no.2, pp. 224-232, 2002.
15. ∞ Controller synthesis of uncertain piecewise continuous-time linear systems", IEE Proc. Control Theory Appl., Vol. 152, no.5, pp. 513-519, 2005.
16. ∞ controller synthesis of uncertain continuous-time piecewise linear systems", IEE Proc. Control Theory Appl., Vol. 151, No. 3, 2004.
17. D. Mignone, G. Ferrari-Trecate, and M. Morari, "Stability and stabilization of piecewise affine and hybrid systems: an LMI approach", IEEE Conference on Decision and Contol, Sydney, Australia, 2000.
18. G. Ferrari-Trecate, F. A. Cuzzola, D. Mignone, and M. Morari, "Analysis of discret-time piecewise affine and hybrid systems", Automatica, vol. 38, pp. 2139-2146, 2002.
19. ∞ analysis and control of discrete-time piecewise affine systems", Int. J. Control., vol. 75, pp. 2193-1301, 2002.
20. J. Xu and L. Xie, "Null controllability of discrete-time planar bimodal piecewise linear systems", Int. J. Control, Vol 78, No. 18, pp. 1486-1496, 2005.
21. M. C. de Oliveira, J. Bernussou and J. C. Geromel, "A new discrete-time robust stability condition", Systems and Control Letters, vol. 37, pp. 261-265, 1999.
22. ∞ norm characterizations and controller parametrizations for discrete-time systems", Int. J. Control, vol. 75, pp. 666-679, 2002.
23. 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations", IEEE Trans. Automat. Contr., Vol. 46, no.12, pp. 1941-1946, 2001.
24. S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA: SIAM, 1994.
25. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, The LMI Control Toolbox. Natick, MA: Mathworks, 1995.