Robust H2 and H∞ filter design for uncertain linear systems via LMIs and polynomial matrices

Signal Processing

Volumn 91, Issue 5, 2011, Pages 1115-1122

  Lacerda, Márcio J ^a   Oliveira, Ricardo C L F ^a   Peres, Pedro L D ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Linear matrix inequalities; Robust H2 and H filtering; Uncertain systems

Indexed keywords

BELONG TO; DISCRETE-TIME; EXISTING METHOD; FILTER DESIGNS; NUMERICAL COMPARISON; OPTIMIZATION PROCEDURES; POLYNOMIAL MATRICES; POLYTOPES; ROBUST FILTERS; ROBUST H; TIME INVARIANTS; UNCERTAIN LINEAR SYSTEM; UNCERTAIN PARAMETERS;

CONTINUOUS TIME SYSTEMS; CONVEX OPTIMIZATION; DESIGN; FILTER BANKS; LINEAR SYSTEMS; NUMERICAL METHODS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

LINEAR MATRIX INEQUALITIES;

EID: 79551472173     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2010.10.013     Document Type: Article

References (40)

1. B.D.O. Anderson, and J.B. Moore Optimal Filtering 1979 Prentice-Hall Englewood, NJ
2. J.C. Geromel Optimal linear filtering under parameter uncertainty IEEE Transactions on Signal Processing 47 1 1999 168 175
3. C.E. de Souza, and A. Trofino A linear matrix inequality approach to the design of robust H 2 filters L. El Ghaoui, S.I. Niculescu, Advances in Linear Matrix Inequality Methods in Control, Advances in Design and Control 2000 SIAM Philadelphia, PA 175 185
4. J.C. Geromel, and M.C. de Oliveira H 2 and H ∞ robust filtering for convex bounded uncertain systems IEEE Transactions on Automatic Control 46 1 2001 100 107
5. J.C. Geromel, J. Bernussou, G. Garcia, and M.C. de Oliveira H 2 and H ∞ robust filtering for discrete-time linear systems SIAM Journal on Control and Optimization 38 5 2000 1353 1368
6. R.M. Palhares, P.L.D. Peres, Robust H ∞ filtering design with pole constraints for discrete-time systems: an LMI approach, in: Proceedings of the 1999 American Control Conference, vol. 1, San Diego, CA, 1999, pp. 44184422.
7. R.M. Palhares, and P.L.D. Peres Robust H ∞ filtering design with pole placement constraint via LMIs Journal of Optimization Theory and Applications 102 2 1999 239 261
8. C.E. de Souza, R.M. Palhares, and P.L.D. Peres Robust H ∞ filter design for uncertain linear systems with multiple time-varying state delays IEEE Transactions on Signal Processing 49 3 2001 569 576
9. R.M. Palhares, C.E. de Souza, and P.L.D. Peres Robust H ∞ filtering for uncertain discrete-time state-delayed systems IEEE Transactions on Signal Processing 49 8 2001 1096 1703
10. R.M. Palhares, and P.L.D. Peres Robust filtering with guaranteed energy-to-peak performancean LMI approach Automatica 36 6 2000 851 858
11. J.C. Geromel, M.C. de Oliveira, and J. Bernussou Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions SIAM Journal on Control and Optimization 41 3 2002 700 711
12. L. Xie, L. Lu, D. Zhang, and H. Zhang Improved robust H 2 and H ∞ filtering for uncertain discrete-time systems Automatica 40 5 2004 873 880
13. H.D. Tuan, P. Apkarian, and T.Q. Nguyen Robust and reduced-order filtering: new LMI-based characterizations and methods IEEE Transactions on Signal Processing 49 12 2001 2975 2984
14. K.A. Barbosa, C.E. de Souza, and A. Trofino Robust H 2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions Systems & Control Letters 54 3 2005 251 262
15. Z. Duan, J. Zhang, C. Zhang, and E. Mosca A simple design method of reduced-order filters and its applications to multirate filter bank design Signal Processing 86 5 2006 1061 1075
16. Z.S. Duan, J.X. Zhang, C.S. Zhang, and E. Mosca Robust H 2 and H ∞ filtering for uncertain linear systems Automatica 42 11 2006 1919 1926
17. W.A. Zhang, L. Yu, and X.F. Jiang Delay-dependent generalized H 2 filtering for uncertain systems with multiple time-varying state delays Signal Processing 87 4 2007 709 724
18. R.A. Borges, V.F. Montagner, R.C.L.F. Oliveira, P.L.D. Peres, and P.-A. Bliman Parameter-dependent H 2 and H ∞ filter design for linear systems with arbitrarily time-varying parameters in polytopic domains Signal Processing 88 7 2008 1801 1816
19. C. Chen, H. Liu, and X. Guan H ∞ filtering of time-delay TS fuzzy systems based on piecewise LyapunovKrasovskii functional Signal Processing 89 10 2009 1998 2005
20. H. Dong, Z. Wang, and H. Gao H ∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links Signal Processing 89 8 2009 1567 1575
21. Y. He, G.-P. Liu, D. Rees, and M. Wu H ∞ filtering for discrete-time systems with time-varying delay Signal Processing 89 3 2009 275 282
22. Y. Chen, A. Xue, and S. Zhou New delay-dependent L 2 L ∞ filter design for stochastic time-delay systems Signal Processing 89 6 2009 974 980
23. M.V. Basin, P. Shi, and D. Calderon-Alvarez Central suboptimal H ∞ filter design for nonlinear polynomial systems International Journal of Adaptive Control and Signal Processing 23 10 2009 926 939
24. M.V. Basin, P. Shi, D. Calderon-Alvarez, and J. Wang Central suboptimal H ∞ filter design for linear time-varying systems with state or measurement delay Circuits Systems and Signal Processing 28 2 2009 305 330
25. M.V. Basin, P. Shi, and D. Calderon-Alvarez Central suboptimal H ∞ filter design for linear time-varying systems with state or measurement delay International Journal of Systems Science 41 4 2010 411 421
26. R.A. Borges, R.C.L.F. Oliveira, C.T. Abdallah, and P.L.D. Peres H ∞ filtering for discrete-time linear systems with bounded time-varying parameters Signal Processing 90 1 2010 282 291
27. 2 filters for uncertain systems Systems & Control Letters 57 7 2008 585 593
28. M.J. Lacerda, R.C.L.F. Oliveira, P.L.D. Peres, Robust H 2 filter design for polytopic linear systems via LMIs and polynomial matrices, in: Proceedings of the 49th IEEE Conference on Decision and Control, December 1517, 2010, Atlanta, GA, USA.
29. E.N. Gonalves, R.M. Palhares, and R.H.C. Takahashi H 2 / H ∞ filter design for systems with polytope-bounded uncertainty IEEE Transactions on Signal Processing 54 9 2006 3620 3626
30. J.C. Geromel, and R.H. Korogui H 2 robust filter design with performance certificate via convex programming Automatica 44 4 2008 937 948
31. S.P. Boyd, and C.H. Barratt Linear Control Design: Limits of Performance 1991 Prentice-Hall Englewood Cliffs, NJ, USA
32. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, PA, 1994.
33. R.C.L.F. Oliveira, and P.L.D. Peres A convex optimization procedure to compute H 2 and H ∞ norms for uncertain linear systems in polytopic domains Optimal Control Applications and Methods 29 4 2008 295 312
34. M.C. de Oliveira, and R.E. Skelton Stability tests for constrained linear systems S.O. Reza Moheimani, Perspectives in Robust Control of Lecture Notes in Control and Information Science vol. 268 2001 Springer-Verlag New York 241 257
35. Z. Duan, J. Wang, and L. Huang Parameter-dependent Lyapunov function method for a class of uncertain nonlinear systems with multiple equilibria Circuits Systems and Signal Processing 26 2 2007 147 164
36. R.C.L.F. Oliveira, and P.L.D. Peres Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations IEEE Transactions on Automatic Control 52 7 2007 1334 1340
37. J. Lfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, 2004, pp. 284289, 〈 http://control.ee.ethz. ch/∼joloef/yalmip.php 〉.
38. J.F. Sturm Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optimization Methods and Software 11 1 1999 625 653 〈 http://sedumi.mcmaster.ca/ 〉
39. S.H. Jin, and J.B. Park Robust H ∞ filtering for polytopic uncertain systems via convex optimisation IEE ProceedingsControl Theory and Applications 148 1 2001 55 59
40. H. Gao, X. Meng, and T. Chen H ∞ filter design for discrete delay systems: a new parameter-dependent approach International Journal of Control 82 6 2009 993 1005