Abstract
This paper is concerned with the problem of non-fragile H 2 and H ∞ filter designs for two-dimensional (2-D) discrete systems in Roesser model with polytopic uncertainties. The filters to be designed are assumed to be with additive norm-bounded coefficient variations which reflect the imprecision in filter implementation. The complicated filter design problem is successfully tackled by using the slack variable technique and imposing a structural restriction on the slack matrix. Explicit expressions of the non-fragile H 2 and H ∞ filters are given in terms of solutions to a set of linear matrix inequalities (LMIs). An illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.
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References
Che W., Yang G. (2008) Non-fragile H ∞ filtering for discrete-time systems with finite word length consideration. Acta Automatica Sinica 34: 886–892
Du C., Xie L. (2002) H ∞ Control and filtering of two-dimensional systems. Springer, Heidelberg
Du C., Xie L., Zhang C. (2000) Solutions for H ∞ filtering of two-dimensional systems. Multidimensional Systems and Signal Processing 11: 301–320
Duan Z., Zhang J., Zhang C., Mosca E. (2006) Robust H 2 and H ∞ filtering for uncertain linear systems. Automatica 42: 1919–1926
Fornasini E., Marchesini G. (1976) State-space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control 21: 484–492
Gahinet P., Nemirovski A., Laub A. J., Chilali M. (1995) LMI control toolbox. The MathWorks Inc, Natick,MA
Gao C., Duan G., Meng X. (2008a) Robust H ∞ filter design for 2D discrete systems in Roesser model. International Journal of Automation and Computing 5: 413–418
Gao H., Lam J., Wang C., Xu S. (2004) Robust H ∞ filtering for 2D stochastic systems. Circuits, Systems, and Signal Processing 23: 479–505
Gao H., Meng X., Chen T. (2008b) New design of robust H ∞ filters for 2-D systems. IEEE Signal Processing Letters 15: 217–220
Geromel J. C., de Oliveira M. C., Bernussou J. (2002) Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions. SIAM Journal of Control Optimization 41: 700–711
Kaczorek T. (1985) Two-dimensional linear systems. Springer, Berlin
Katayama H., Kosaka M. (1979) Recursive filtering algorithm for a 2-D system. IEEE Transactions on Automatic Control 24: 130–132
Khargonekar P. P., Petersen I. R., Zhou K. (1990) Robust stabilization of uncertain linear systems: Quadratic stabilizability and H ∞ control theory. IEEE Transactions on Automatic Control 35: 356–361
Kurek J. E. (1985) The general state-space model for a two-dimensional linear digital system. IEEE Transactions on Automatic Control 30: 600–602
Lin Z., Bruton L. T. (1989) BIBO stability of inverse 2-D digital filters in the presence of nonessential singularities of the second kind. IEEE Transactions on Circuits and Systems 36: 244–254
Liu X., Gao H., Shi P. (2009) Robust H ∞ filtering for 2-D systems with intermittent measurements. Circuits, Systems, and Signal Processing 28: 283–303
Mahmoud M. S. (2004) Resilient linear filtering of uncertain systems. Automatica 40: 1797–1802
Roesser R. P. (1975) A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control 20: 1–10
Song B., Xu S., Zou Y. (2009) Non-fragile H ∞ filtering for uncertain stochastic time-delay systems. International Journal of Innovative Computing, Information and Control 5: 2257–2265
Tuan H. D., Apkarian P., Nguyen T. Q., Narikiyo T. (2002) Robust mixed H 2/H ∞ filtering of 2-D systems. IEEE Transactions on Signal Processing 50: 1759–1771
Xie L., Lu L., Zhang D., Zhang H. (2004) Improved robust H 2 and H ∞ filtering for uncertain discrete-time systems. Automatica 40: 873–880
Xu H., Zou J., Lu J., Xu S. (2005) Robust H ∞ control for a class of uncertain nonlinear two-dimensional systems with state delays. Journal of Franklin Institute 342: 877–891
Xu S., Chen T. (2003) Robust H ∞ filtering for uncertain impulsive stochastic systems under sampled measurements. Automatica 39: 509–516
Xu S., Chen T. (2004) An LMI approach to the H ∞ filter design for uncertain systems with distributed delays. IEEE Transactions on Circuits and Systems II 51: 195–201
Xu S., van Dooren P. (2002) Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty. International Journal of Control 75: 766–774
Yang G., Che W. (2008) Non-fragile H ∞ filter design for linear continuous-time systems. Automatica 44: 2849–2856
Yang G., Wang J. (2001) Robust nonfragile Kalman filtering for uncertain linear systems with estimatior gain uncertainty. IEEE Transactions on Automatic Control 46: 343–348
Yang R., Xie L., Zhang C. (2006) H 2 and mixed H 2 /H ∞ control of two-dimensional systems in Roesser model. Automatica 42: 1507–1514
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Xu, H., Lin, Z. & Makur, A. Non-fragile H 2 and H ∞ filter designs for polytopic two-dimensional systems in Roesser model. Multidim Syst Sign Process 21, 255–275 (2010). https://doi.org/10.1007/s11045-010-0104-5
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DOI: https://doi.org/10.1007/s11045-010-0104-5