Stability analysis of second-order switched homogeneous systems

SIAM Journal on Control and Optimization

Volumn 41, Issue 5, 2003, Pages 1609-1625

  Holcman, David ^a   Margaliot, Michael ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Absolute stability; Hybrid control; Hybrid systems; Robust stability; Switched linear systems

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS); SWITCHING;

HYBRID CONTROL;

SYSTEM STABILITY;

EID: 0141869041     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901389354     Document Type: Article

References (20)

1. F. BLANCHINI, Set invariance in control, Automatica, 35 (1999), pp. 1747-1767.
2. V. D. BLONDEL AND J. N. TSITSIKLIS, A survey of computational complexity results in systems and control, Automatica, 36 (2000), pp. 1249-1274.
3. U. BOSCAIN, Stability of planar switched systems: The linear single input case, SIAM J. Control Optim., 41 (2002), pp. 89-112.
4. S. BOYD, L. EL GHAOUI, E. FERON, AND V. BALAKRISHNAN, Linear Matrix Inequalities in System and Control Theory, SIAM Stud. Appl. Math. 15, SIAM, Philadelphia, 1994.
5. R. W. BROCKETT, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. J. Sussmann, eds., Birkhäuser, Boston, 1983, pp. 181-191.
6. W. P. DAYAWANSA AND C. F. MARTIN, A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE Trans. Automat. Control, 44 (1999), pp. 751-760.
7. A. F. FILIPPOV, Stability conditions in homogeneous systems with arbitrary regime switching, Automat. Remote Control, 41 (1980), pp. 1078-1085.
8. H. GOLDSTEIN, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA, 1980.
9. W. HAHN, Stability of Motion, Springer-Verlag, New York, 1967.
10. J. H. HUBBARD AND B. H. WEST, Differential Equations: A Dynamical Systems Approach. Higher-Dimensional Systems, Springer-Verlag, New York, 1995.
11. D. LIBERZON AND A. S. MORSE, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine, 19 (1999), pp. 59-70.
12. Y. LIN, E. D. SONTAG, AND Y. WANG, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim., 34 (1996), pp. 124-160.
13. J. L. MANCILLA-AGUILAR AND R. A. GARCIA, A converse Lyapunov theorem for nonlinear switched systems, Systems Control Lett., 41 (2000), pp. 67-71.
14. M. MARGALIOT AND G. LANGHOLZ, Necessary and sufficient conditions for absolute stability: The case of second-order systems, IEEE Trans. Circuits Systems I Fund. Theory Appl., to appear.
15. A. S. MORSE, ED., Control Using Logic-Based Switching, Lecture Notes in Control and Inform. Sci. 222, Springer-Verlag, London, 1997.
16. E. S. PYATNITSKIY AND L. B. RAPOPORT, Criteria of asymptotic stability of differential inclusions and periodic motions of time-varying nonlinear control systams, IEEE Trans. Circuits Systems I Fund. Theory Appl., 43 (1996), pp. 219-229.
17. L. B. RAPOPORT, Asymptotic stability and periodic motions of selector-linear differential inclusions, in Robust Control via Variable Structure and Lyapunov Techniques, Lecture Notes in Control and Inform. Sci. 217, F. Garofalo and L. Glielmo, eds., Springer-Verlag, London, 1996, pp. 269-285.
18. A. J. VAN DER SCHAFT AND H. SCHUMACHER, An Introduction to Hybrid Dynamical Systems, Lecture Notes in Control and Inform. Sci. 251, Springer-Verlag, London, 2000.
19. M. VIDYASAGAR, Nonlinear Systems Analysis, Prentice-Hall, Upper Saddle River, NJ, 1993.
20. A. L. ZELENTSOVSKY, Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems, IEEE Trans. Automat. Control, 39 (1994), pp. 135-138.