Lie algebras and stability of switched nonlinear systems

Unsolved Problems in Mathematical Systems and Control Theory

Volumn 9781400826155, Issue , 2009, Pages 203-207

  Liberzon, Daniel ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

LIE ALGEBRA; SWITCHED NON-LINEAR SYSTEMS;

CONTROL ENGINEERING;

EID: 84884860951     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (12)

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2. D. Angeli and D. Liberzon, " A note on uniform global asymptotic stability of nonlinear switched systems in triangular form," In: Proc. 14th Int. Symp. on Mathematical Theory of Networks and Systems (MTNS), 2000.
3. P. E. Crouch, "Dynamical realizations of finite Volterra series," SIAM J. Control Optim., 19:177-202, 1981.
4. L. Gurvits, "Stability of discrete linear inclusion," Linear Algebra Appl., 231:47-85, 1995.
5. M. Kawski, "Nilpotent Lie algebras of vectorfields'," J. Reine Angew. Math., 388:1-17, 1988.
6. D. Liberzon, J. P. Hespanha, and A. S. Morse, "Stability of switched systems: a Lie-algebraic condition," Systems Control Lett., 37:117-122, 1999.
7. D. Liberzon, Switching in Systems and Control. Birkhäuser, Boston, 2003.
8. J. L. Mancilla-Aguilar, "A condition for the stability of switched nonlinear systems," IEEE Trans. Automat. Control, 45:2077-2079, 2000.
9. A. Marigo, "Constructive necessary and sufficient conditions for strict triangularizability of driftless nonholonomic systems'," In: Proc. 38th IEEE Conf. on Decision and Control, pages 2138-2143, 1999.
10. K. S. Narendra and J. Balakrishnan, "A common Lyapunov function for stable LTI systems with commuting A-matrices," IEEE Trans. Automat. Control, 39:2469-2471, 1994.
11. H. Samelson, Notes on Lie Algebras. Van Nostrand Reinhold, New York, 1969.
12. H. Shim, D. J. Noh, and J. H. Seo, "Common Lyapunov function for exponentially stable nonlinear systems," In: Proc. 4th SIAM Conference on Control and its Applications, 1998.