Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions

Systems and Control Letters

Volumn 55, Issue 1, 2006, Pages 8-16

  Margaliot, Michael ^a   Liberzon, Daniel ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Differential inclusion; Global asymptotic stability; Lie bracket; Maximum principle; Optimal control; Switched nonlinear system

Indexed keywords

ASYMPTOTIC STABILITY; MAXIMUM PRINCIPLE; OPTIMAL CONTROL SYSTEMS; SWITCHES; SWITCHING; SYSTEM STABILITY; VECTORS;

DIFFERENTIAL INCLUSION; GLOBAL ASYMPTOTIC STABILITY; LIE BRACKET; SWITCHED NONLINEAR SYSTEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 28444484618     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2005.04.011     Document Type: Article

References (27)

1. A.A. Agrachev, and D. Liberzon Lie-algebraic stability criteria for switched systems SIAM J. Control Optim. 40 2001 253 269
2. A.A. Agrachev, and Yu.L. Sachkov Control Theory from the Geometric Viewpoint 2004 Springer Berlin
3. A.A. Agrachev, and S.A. Vakhrameev Nonlinear control systems of constant rank and bang-bang conditions for extremal controls Soviet Math. Dokl. 30 1984 620 624
4. J.-P. Aubin, and A. Cellina Differential Inclusions: Set-Valued Maps and Viability Theory 1984 Springer Berlin
5. U. Boscain Stability of planar switched systems: the linear single input case SIAM J. Control Optim. 41 2002 89 112
6. A.F. Filippov Differential Equations with Discontinuous Righthand Sides 1988 Kluwer Dordrecht
7. L. Gurvits Stability of discrete linear inclusion Linear Algebra Appl. 231 1995 47 85
8. D. Holcman, and M. Margaliot Stability analysis of switched homogeneous systems in the plane SIAM J. Control Optim. 41 5 2003 1609 1625
9. V. Jurdjevic Geometric Control Theory 1996 Cambridge University Press Cambridge
10. D. Liberzon Switching in Systems and Control 2003 Birkhäuser Boston
11. D. Liberzon Lie algebras and stability of switched nonlinear systems V. Blondel A. Megretski Unsolved Problems in Mathematical Systems and Control Theory 2004 Princeton University Press NJ 203 207
12. D. Liberzon, J.P. Hespanha, and A.S. Morse Stability of switched systems: a Lie-algebraic condition Systems Control Lett. 37 1999 117 122
13. Y. Lin, E.D. Sontag, and Y. Wang A smooth converse Lyapunov theorem for robust stability SIAM J. Control Optim. 34 1996 124 160
14. J.L. Mancilla-Aguilar A condition for the stability of switched nonlinear systems IEEE Trans. Automat. Control 45 2000 2077 2079
15. M. Margaliot, and R. Gitizadeh The problem of absolute stability: a dynamic programming approach Automatica 40 2004 1247 1252
16. M. Margaliot, and G. Langholz Necessary and sufficient conditions for absolute stability: the case of second-order systems IEEE Trans. Circuits Systems-I 50 2003 227 234
17. K.S. Narendra, and J. Balakrishnan A common Lyapunov function for stable LTI systems with commuting A -matrices IEEE Trans. Automat. Control 39 1994 2469 2471
18. R.S. Palais A global formulation of the Lie theory of transformation groups Mem. Amer. Math. Soc. 22 1957 1 123
19. E.S. Pyatnitskiy, and L.B. Rapoport Criteria of asymptotic stability of differential inclusions and periodic motions of time-varying nonlinear control systems IEEE Trans. Circuits Systems-I 43 1996 219 229
20. L.B. Rapoport, Asymptotic stability and periodic motions of selector-linear differential inclusions, in: F. Garofalo, L. Glielmo (Eds.), Robust Control via Variable Structure and Lyapunov Techniques, LNCIS 217, Springer, Berlin, 1996, pp. 269-285.
21. H. Shim, D.J. Noh, and J.H. Seo Common Lyapunov function for exponentially stable nonlinear systems J. Korean Institute of Electrical Engineers 11 2001 108 111 (Presented at the 4th SIAM Conf. on Control and its Applications, 1998)
22. M. Sigalotti Local regularity of optimal trajectories for control problems with general boundary conditions J. Dynam. Control Systems 11 2005 91 123
23. H.J. Sussmann A bang-bang theorem with bounds on the number of switchings SIAM J. Control Optim. 17 1979 629 651
24. H.J. Sussmann Lie brackets, real analyticity and geometric control R.W. Brockett R.S. Millman H.J. Sussmann Differential Geometric Control Theory 1983 Birkhäuser Boston 1 116
25. S.A. Vakhrameev A bang-bang theorem with a finite number of switchings for nonlinear smooth control systems J. Math. Sci. 85 1997 2002 2016
26. R. Vinter Optimal Control 2000 Birkhäuser Boston
27. L. Vu, and D. Liberzon Common Lyapunov functions for families of commuting nonlinear systems Systems Control Lett. 54 2005 405 416