A generating function approach to the stability of discrete-time switched linear systems

HSCC'10 - Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

Volumn , Issue , 2010, Pages 273-282

  Hu, Jianghai ^a   Shen, Jinglai ^b   Zhang, Wei ^c  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exponential stability; Generating functions; Switched linear systems

Indexed keywords

DISCRETE-TIME; EXPONENTIAL GROWTH RATES; EXPONENTIAL STABILITY; GENERATING FUNCTION APPROACH; GENERATING FUNCTIONS; NUMERICAL ALGORITHMS; SUFFICIENT CONDITIONS; SWITCHED LINEAR SYSTEM;

COMPUTATION THEORY; ELECTRIC GROUNDING; FUNCTION EVALUATION; HYBRID COMPUTERS; HYBRID SYSTEMS; LINEAR SYSTEMS; SWITCHING FUNCTIONS; SWITCHING SYSTEMS; SYSTEM STABILITY;

EXPONENTIAL FUNCTIONS;

EID: 77953042953     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1755952.1755991     Document Type: Conference Paper

References (18)

1. N. E. Barabanov. A method for calculating the Lyapunov exponent of a differential inclusion. Automat. Remote Control, 50:475-479, 1989.
2. V. Blondel, J. Theys, and Y. Nesterov. Approximations of the rate of growth of switched linear systems. In R. Alur and G. Pappas, editors, Hybrid Systems: Computation and Control: 7th Int. Workshop, Philadelphia, PA, pages 173-186. Springer-Verlag, Mar. 2004.
3. M. S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43(4):475-482, 1998.
4. F. H. Clarke. Optimization and Nonsmooth Analysis. SIAM Press, 1990.
5. F. Facchinei and J. S. Pang. Finite-Dimensional Variational Inequalities and Complementarity Problems. Spring-Verlag, New York, 2003.
6. J. P. Hespanha and A. S. Morse. Stability of switched systems with average dwell time. In Proc. 38th IEEE Int. Conf. Decision and Control, pages 2655-2660, Phoenix, AZ, 1999.
7. J. Hu, J. Shen, and W. Zhang. Generating functions of switched linear systems: analysis, computation and stability application. IEEE Trans. Automatic Control, 2010. Submitted.
8. T. Hu, L. Ma, and Z. Lin. Stabilization of switched systems via composite quadratic functions. IEEE Trans. Automat. Contr., 53(11):2571-2585, 2008.
9. M. Johansson and A. Rantzer. Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Automat. Contr., 43(4):555-559, 1998. (Pubitemid 128737378)
10. S. G. Krantz and H. Parks. A Primer of Real Analytic Functions. Birkhäuser-Verlag, Boston, 2nd edition, 2002.
11. D. Liberzon. Switching in Systems and Control. Birkhäuser, Boston, MA, 2003.
12. D. Liberzon, J. P. Hespanha, and A. S. Morse. Stability of switched linear systems: A Lie-algebraic condition. Syst. Control Lett., 37(3):117-122, 1999. (Pubitemid 129608440)
13. H. Lin and P. Antsaklis. Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Trans. Automat. Contr., 54(2):308-322, 2009.
14. J. Shen and J. Hu. Stability of discrete-time conewise linear inclusions and switched linear systems. To appear in American Control Conference, Baltimore, MD, 2010.
15. R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King. Stability criteria for switched and hybrid systems. SIAM Review, 49(4):545-592, 2007.
16. J. Theys. Joint Spectral Radius: Theory and Approximations. PhD thesis, Universite Catholique de Louvain, 2005.
17. F. Wirth. The generalized spectral radius and extremal norms. Linear Algebra Appl., 342(1-3):17-40, 2002.
18. C. Yfoulis and R. Shorten. A numerical technique for stability analysis of linear switched system. In R. Alur and G. Pappas, editors, Hybrid Systems: Computation and Control: 7th Int. Workshop, Philadelphia, PA, pages 631-645. Springer-Verlag, Mar. 2004.