SOS for sampled-data systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 44, Issue 1 PART 1, 2011, Pages 1441-1446

  Seuret, Alexandre ^a   Peet, Matthew M ^b  

^a CNRS   (France)

^b Illinois Institute of Technology   (United States)

Author keywords

Lyapunov function; Sampled data systems; Sum of squares

Indexed keywords

LINEAR SYSTEMS; LYAPUNOV FUNCTIONS;

ASYNCHRONOUS SAMPLING; CONVEX CONSTRAINTS; FUNCTIONAL VARIABLE; SAMPLED DATA SYSTEMS; SAMPLED-DATA INPUTS; STABILITY ANALYSIS; STABILITY CONDITION; SUM OF SQUARES;

SAMPLED DATA CONTROL SYSTEMS;

EID: 84866775367     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20110828-6-IT-1002.00824     Document Type: Conference Paper

References (24)

1. T. Chen and B.A. Francis. Optimal sampled-data control systems. Springer-Verlag, Berlin, Germany, 1995.
2. E. Fridman. A refined input delay approach to sampled-data control. Automatica, 46(2):421-427, 2010.
3. E. Fridman, A. Seuret, and J.-P. Richard. Robust sampleddata stabilization of linear systems: An input delay approach. Automatica, 40(8):1141-1446, 2004.
4. H. Fujioka. Stability analysis of systems with aperiodic sampleand- hold devices. Automatica, 45(3):771-775, 2009.
5. K. Gu, V.-L. Kharitonov, and J. Chen. Stability of time-delay systems. Birkhauser, 2003.
6. J.P. Hespanha, P. Naghshtabrizi, and Y. Xu. A survey of recent results in networked control systems. Proceedings of the IEEE, 95(1):138-162, 2007.
7. L. Hetel. Robust stability and control of switched linear systems. Phd, Institut National Polytechnique de Lorraine - INPL, Nancy France, 2007.
8. L. Hetel, J. Daafouz, and C. Iung. Stabilization of arbitrary switched linear systems with unknown time-varying delays. IEEE Trans. on Automatic Control, 51(10):1668-1674, Oct. 2006.
9. K. Liu and E. Fridman. Discontinuous Lyapunov functionals for linear systems with sawtooth delays. In Proc. of the 8th IFAC Workshop on Time-Delay Systems, September 2009.
10. W. Michiels, S.-I. Niculescu, and L. Moreau. Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems : a comparison. IMA Journal of Mathematical Control and Information, 21(4):393-418,2004.
11. L. Mirkin. Some remarks on the use of time-varying delay to model sample-and-hold circuits. IEEE Trans. on Automatic Control, 52(6):1009-1112, 2007.
12. P. Naghshtabrizi, J.P. Hespanha, and A.R. Teel. Exponential stability of impulsive systems with application to uncertain sampled-data systems. Systems and Control Letters, 57(5): 378-385, 2008.
13. Y. Oishi and H. Fujioka. Stability and stabilization of aperiodic sampled-data control systems: An approach using robust linear matrix inequalities. In Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, December 16-18 2009.
14. P. A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, 2000.
15. M.M. Peet, A. Papachristodoulou, and S. Lall. Positive forms and stability of linear time-delay systems. SIAM Journal on Control and Optimization, 47(6):3227-3258, 2009.
16. S. Prajna, A. Papachristodoulou, and P. A. Parrilo. Introducing SOSTOOLS: a general purpose sum of squares programming solver. Proceedings of the IEEE Conference on Decision and Control, 2002.
17. M. Putinar. Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J., 42(3):969-984, 1993.
18. A. Seuret. Stability analysis for sampled-data systems with a time-varying period. In Proc. of the 48th IEEE Conference on Decision and Control, December 2009.
19. A. Seuret. A novel stability analysis of linear systems under asynchronous samplings. Accepted in Automatica, 2011.
20. J. F. Sturm. Using SeDuMi 1.02, a Matlab Toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12:625-653, 1999.
21. Y.S. Suh. Stability and stabilization of nonuniform sampling systems. Automatica, 44(12):3222-3226, 2008.
22. S. Zampieri. A survey of recent results in Networked Control Systems. In Proc. of the 17th IFAC World Congress, Seoul, Korea, July 2008.
23. W. Zhang and M.S. Branicky. Stability of networked control systems with time-varying transmission period. In Allerton Conf. Communication, Control, and Computing, October 2001.
24. W. Zhang, M.S. Branicky, and S.M. Phillips. Stability of networked control systems. IEEE Control Systems Magazine, (21), 2001.