ℋ∞ and l2-l∞ filtering for two-dimensional linear parameter-varying systems

International Journal of Robust and Nonlinear Control

Volumn 17, Issue 12, 2007, Pages 1129-1154

  Wu, Ligang ^a   Wang, Zidong ^b   Gao, Huijun ^a   Wang, Changhong ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

L2 l filtering; Linear parameter varying (LPV) systems; Parameterized linear matrix inequalities (PLMIs); filtering; Two dimensional (2 D) systems

Indexed keywords

LINEAR MATRIX INEQUALITIES; MATHEMATICAL MODELS; PARAMETERIZATION; PROBLEM SOLVING; STATE SPACE METHODS;

CONVEX OPTIMIZATION; LINEAR PARAMETER VARYING (LPV) SYSTEMS; TWO DIMENSIONAL SYSTEMS;

LINEAR SYSTEMS;

EID: 34547232586     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1169     Document Type: Article

References (33)

1. Anderson BDO, Moore JB. Optimal Filtering. Prentice-Hall: Englewood Cliffs, NJ, 1979.
2. Wang Z, Yang F, Liu X. Robust filtering for systems with stochastic nonlinearities and deterministic uncertainties. Proceedings of the IMechE - Journal of Systems and Control Engineering 2006; 220(3): 171-182.
3. ∞ filtering for LPV systems with both discrete and distributed delays. IEE Proceedings - D Control Theory and Applications 2006; 153(4):483-492.
4. ∞ filtering for nonlinear singularly perturbed systems with pole placement constraints: an LMI approach. IEEE Transactions on Signal Processing 2004; 34(6): 1659-1667.
5. ∞ filter for Markovian jumping systems with time delay. IEEE Transactions on Circuits and Systems: Part II 2004; 51(11):607-612.
6. ∞ filtering for stochastic time-delay systems with missing measurements. IEEE Transactions on Signal Processing 2006; 54(7):2579-2587.
7. ∞ filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Transactions on Signal Processing 2004; 52(11):3200-3212.
8. ∞ prediction with application to systems with delayed measurements. Automatica 2004; 40(7):1253-1261.
9. ∞ filtering for a class of uncertain nonlinear time-delay systems. IEEE Transactions on Automatic Control 2003; 48(9):1661-1666.
10. Palhares RM, Peres PLD. Robust filtering with guaranteed energy-to-peak performance: an LMI approach. Automatica 2000; 36(6):851-858.
11. Vincent T, Abedor J, Nagpal K, Khargonekar RP. Discrete-time estimators with guaranteed peak-to-peak performance. Proceedings of the 13th IFAC Triennial World Congress, San Francisco, CA, U.S.A., 1996; 43-48.
12. Wu F, Grigoriadis KM. LPV systems with parameter-varying time delays: analysis and control. Automatica 2001; 37(2):221-229.
13. Shamma JS, Athans M. Analysis of nonlinear gain-scheduled control systems. IEEE Transactions on Automatic Control 1990; 35:898-907.
14. ∞ control of linear parameter-varying systems: a design example. Automatica 1995; 31(7):1251-1261.
15. Gahinet P, Apkarian P, Chilali M. Affine parameter-dependent Lyapunov functions for real parametric uncertainty. IEEE Transactions on Automatic Control 1996; 41:436-442.
16. ∞ filtering for a class of linear parameter-varying systems. IEEE Transactions on Circuits and Systems: Part I 2001; 48(9):1131-1138.
17. 2 gain properties of LPV systems. Proceedings of the American Control Conference, San Diego, CA, U.S.A., 1999; 2262-2266.
18. Emre Kose I, Jabbari F. Control of LPV systems with partly measured parameters. IEEE Transactions on Automatic Control 1999; 44(3):658-663.
19. ∞ gain control of linear parameter-varying systems with parametervarying delays. IEE Proceedings - D Control Theory and Applications 2003; 150(5):509-517.
20. Wang F, Balakrishnan V. Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent system. IEEE Transactions on Automatic Control 2002; 47(5):720-734.
21. Bokor J, Balas B. Detection filter design for LPV systems: a geometric approach. Automatica 2004; 40:511-518.
22. Farhood M, Beck CL, Dullerud GE. On the model reduction of nonstationary LPV systems. Proceedings of the American Control Conference, Denver, Colorado, 2003; 3869-3874.
23. Kaczorek T. Two-Dimensional Linear Systems. Springer: Berlin, Germany, 1985.
24. Lu WS. On a Lyapunov approach to stability analysis of 2-D digital filters. IEEE Transactions on Circuits and Systems: Part I 1994; 41(10):665-669.
25. Paszke W, Lam J, Galkowski K, Xu S, Lin Z. Robust stability and stabilisation of 2D discrete state-delayed systems. Systems and Control Letters 2004; 51(3-4):277-291.
26. ∞ control of two-dimensional Markovian jump systems. IMA Journal of Mathematical Control and Information 2004; 21:377-392.
27. ∞ and robust control of 2-D systems in FM second model. Multidimensional Systems and Signal Processing 2002; 13:256-287.
28. ∞ filtering for uncertain 2-D continuous systems. IEEE Transactions on Signal Processing 2005; 53(5):1731-1738.
29. ∞ model reduction for uncertain two-dimensional discrete systems. Optimal Control Applications and Methods 2005; 26:199-227.
30. de Oliveira MC, Bernussou J, Geromel JC. A new discrete-time robust stability condition. Systems and Control Letters 1999; 37(4):261-265.
31. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. SIAM: Philadelphia, PA, 1994.
32. 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations. IEEE Transactions on Automatic Control 2001; 46(12):1941-1946.
33. ∞ control for time-varying and linear parametrically varying systems. International Journal of Robust and Nonlinear Control 1996; 6(9-10):929-952.