Computation and stability analysis of limit cycles in piecewise linear hybrid systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 36, Issue 6, 2003, Pages 181-186

  Girard, Antoine ^a  

^a LMC   (France)

Author keywords

Hybrid systems; Limit cycles; Poincar map; Stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; HYBRID SYSTEMS; LINEAR SYSTEMS; NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES;

LIMIT-CYCLE; NUMERICAL COMPUTATIONS; PERIODIC SOLUTION; PIECEWISE LINEAR; POINCARE MAP; STABILITY ANALYSIS;

SYSTEM STABILITY;

EID: 85048774266     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/S1474-6670(17)36428-5     Document Type: Conference Paper

References (14)

1. Asarin. E., O. Bournez, T. Dang and O. Maler (2000). Approximate reachability analysis of piecewise linear dynamical systems. In: HSCC'00. pp. 21-31. Number 1790 In: LNCS. Springer Verlag.
2. Girard, A. (2002). Detection of event occurrence in piecewise linear hybrid systems, Proc. of Recent Advances in Soft Computing.
3. Guckenheimcr, J. and B. Meloon (2000). Computing periodic orbits and their bifurcations with automatic differentiation, SIAM J. Set. Compui, 22, 951-980.
4. Hiskens. LA. (2001a). Stability of hybrid system limit cycles: application to the compass gait biped robot. Proc. of the 40th IEEE Conf. on Decision and Control pp. 774-779.
5. Hiskens, I. A. (2001b). Stability of limit cycles in hybrid systems. Proc. of the 34th Hawaii Int. Conf. on System Sciences.
6. Hiskens, I. A. and M. A. Pai (2000), Trajectory sensitivity analysis of hybrid systems. IEEE Tratls. on Circuits and Systems 47(2), 204-220.
7. Johansson, M. and A. Rantzer (1998). Computation of piecewise quadratic lyapunov functions for hybrid systems. IEEE Trans, m Automatic Control 43(4), 555-559
8. Llibre, J., E. Nunez and A. E. Teruel (2002). Limit cycles for planar piecewise linear differential systems via first integrals. Qualitative Theory of Dynamical Systems 3(1), 29-50.
9. Matveev, A. S. and A. V. Savkin (2000). Qualitative Theory of Hybrid Dynamical Systems (Control and Engineering). Birkhauser.
10. Pcttit, N. B. O. L and P. E. Wellstead (2000). Analysing piecewise linear dynamical systems. IEEE Control Systems 15(5), 43-50.
11. Rubensson, M. and B. Lennartson (2000). Stability of limit cycles in hybrid systems using discrete-time lyapunov techniques. Proc. of the 39th IEEE Conf. on Decision and Control pp. 1397-1402.
12. Rubensson, M., B. Lennartson and S. Pettersson (1998). Convergence to limit cycies in hybrid systems: an example. Large Scale Systems: Theory and Applications pp. 704-709.
13. Simic, S. N., K. H. Johansson, J. Lygeros and S. Sastry (2002). Hybrid limit cycles and hybrid poincare-bendixon. IFAC world congress.
14. Viswanath, D. (2001). The lindsledt-poincare technique as an algorithm for computing periodic orbits. SIAM Review 43(3), 478-495.