Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

Automatica

Volumn 46, Issue 4, 2010, Pages 687-694

  Shu, Zhan ^a,b   Lam, James ^b   Xiong, Junlin ^c  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Linear matrix inequality (LMI); Markovian jump systems; Stabilization; Static output feedback; System augmentation

Indexed keywords

DISCRETE-TIME; DISCRETE-TIME MARKOVIAN JUMP SYSTEM; FEASIBLE SOLUTION; INITIAL VALUES; ITERATION ALGORITHMS; MARKOVIAN JUMP LINEAR SYSTEMS; MARKOVIAN JUMP SYSTEMS; MONOTONIC STRUCTURE; NON-LINEAR MATRIX INEQUALITY; NUMERICAL EXAMPLE; SPECIAL PROPERTIES; STABILIZATION PROBLEMS; STATIC OUTPUT-FEEDBACK; STATIC OUTPUT-FEEDBACK STABILIZATION; SUFFICIENT CONDITIONS; SYSTEM AUGMENTATION; THEORETICAL RESULT;

ALGORITHMS; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; UNCERTAIN SYSTEMS;

STABILIZATION;

EID: 77949284720     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.02.001     Document Type: Article

References (33)

1. ∞ performance for linear discrete-time systems. IEEE Transactions on Automatic Control 50 2 (2005) 250-254
2. Boyd S., El Ghaoui L., Feron E., and Balakrishnan V. Linear matrix inequalities in system and control theory (1994), Society for Industrial and Applied Mathematics, Philadelphia
3. Cao Y., Lam J., and Sun Y. Static output feedback stabilization: An ILMI approach. Automatica 34 12 (1998) 1641-1645
4. Cao Y., Sun Y., and Mao W. A new necessary and sufficient condition for static output feedback stabilizability and comments on: Stabilization via static output feedback. IEEE Transactions on Automatic Control 43 8 (1998) 1110-1111
5. Chizeck H.J., Willsky A.S., and Castanon D. Discrete-time Markovian-jump linear quadratic optimal-control. International Journal of Control 43 1 (1986) 213-231
6. Costa O.L.V., and dePaulo W.L. Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems. Automatica 43 4 (2007) 587-597
7. 2 control of discrete-time Markovian jump linear systems. International Journal of Control 66 4 (1997) 557-579
8. Costa O.L.V., and Fragoso M.D. Stability results for discrete-time linear-systems with Markovian jumping parameters. Journal of Mathematical Analysis and Applications 179 1 (1993) 154-178
9. Costa O.L.V., Fragoso M.D., and Marques R.P. Discrete-time Markov jump linear systems (2005), Springer, London
10. 2-control for discrete-time Markovian jump linear systems. International Journal of Control 73 1 (2000) 11-21
11. ∞-control of discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control 43 1 (1998) 95-100
12. de Oliveira M.C., Bernussou J., and Geromel J.C. A new discrete-time robust stability condition. Systems & Control Letters 37 4 (1999) 261-265
13. de Oliveira, M. C., & Geromel, J. C. (1997). Numerical comparison of output feedback design methods. In Proceedings of the 1997 American control conference, June (pp. 72-76) Vol. 1.
14. de Souza C.E. Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control 51 5 (2006) 836-841
15. 2-control for jump linear systems: Cluster observations of the Markov state. Automatica 38 2 (2002) 343-349
16. ∞ control design for hard disk drives. IEEE Transactions on Control Systems Technology 13 5 (2005) 832-839
17. El Ghaoui L., Oustry F., and AitRami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control 42 8 (1997) 1171-1176
18. Fujimori A. Optimization of static output feedback using substitutive LMI formulation. IEEE Transactions on Automatic Control 49 6 (2004) 995-999
19. ∞ static state-feedback gains: Application to output-feedback design. Automatica 43 9 (2007) 1597-1604
20. ∞ filtering for polytopic discrete-time systems. IEEE Transactions on Signal Processing 53 8 (2005) 3183-3191
21. Geromel, J. C., Peres, P. L. D., & Souza, S. R. (1993). Convex analysis of output feedback structural constraints. In Proceedings of the 32th conference on decision and control, December (pp. 1363-1364). Vol. 2.
22. Huang M., and Dey S. Stability of Kalman filtering with Markovian packet losses. Automatica 43 4 (2007) 598-607
23. Iwasaki T. The dual iteration for fixed-order control. IEEE Transactions on Automatic Control 44 4 (1999) 783-788
24. Ji Y., Chizeck H.J., Feng X., and Loparo K.A. Stability and control of discrete-time jump linear-systems. Control Theory and Advanced Technology 7 2 (1991) 247-270
25. Karan M., Shi P., and Kaya C.Y. Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica 42 12 (2006) 2159-2168
26. Lee J.-W., and Dullerud G.E. Uniform stabilization of discrete-time switched and Markovian jump linear systems. Automatica 42 2 (2006) 205-218
27. ∞ output feedback stabilization of linear discrete-time systems. IEEE Transactions on Automatic Control 51 4 (2006) 675-680
28. Orsi, R. (2005). LMIRank: Software for rank constrained LMI problems. http://users.rsise.anu.edu.au/robert/lmirank/.
29. Orsi R., Helmke U., and Moore J.B. A Newton-like method for solving rank constrained linear matrix inequalities. Automatica 42 11 (2006) 1875-1882
30. Seiler P., and Sengupta R. A bounded real lemma for jump systems. IEEE Transactions on Automatic Control 48 9 (2003) 1651-1654
31. ∞ control of discrete-time Markovian jump systems via static output-feedback controllers. In The 17th IFAC world congress, July (pp. 5909-5914) Vol. 17(1).
32. Syrmos V.L., Abdallah C.T., Dorato P., and Grigoriadis K. Static output feedback-A survey. Automatica 33 2 (1997) 125-137
33. Xiong J., and Lam J. Stabilization of linear systems over networks with bounded packet loss. Automatica 43 1 (2007) 80-87