Abstract
This paper discusses the problem of H∞ model reduction for linear discrete time 2-D singular Roesser models (2-D SRM). A condition for bounded realness is established for 2-D SRM in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition for the solvability of the H∞ model reduction problem is obtained via a group of LMIs and a set of coupling non-convex rank constraints. An explicit parameterization of the desired reduced-order models is presented. Particularly, a simple LMI condition without rank constraints is proposed for the zeroth-order H∞ approximation problem. Finally, a numerical example is given to illustrate the applicability of the proposed approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Zhou Y. Li EB. Lee (1993) ArticleTitle“Model Reduction 2-D Systems with Frequency Error Bounds” IEEE Transactions on Circuits and Systems, II. 40 107–110
H. Kando T. Watanabe H. Vkai Y. Morita (1998) ArticleTitle“A Model Reduction Method of 2D Systems” International Journal of System and Science. 29 IssueID9 989–1005
H. Luo WS. Lu A. Antoniou (1995) ArticleTitle“A Weighted Balanced Approximation for 2-D Discrete Systems and its Application to Model Reduction” IEEE Transactions on Circuits and Systems, II. 42 419–429
C. Du L. Xie YC. Soh (2001) ArticleTitle“H∞ Reduced Order Approximation of 2-D Digital Filters” IEEE Transactions on Circuits and Systems-I. 48 IssueID6 688–698
S. Xu J. Lam (2003) ArticleTitle“H∞ Model Reduction for Discrete-Time Singular Systems” Systems and Control Letters. 48 121–133
T. Kaczorek (1988) ArticleTitle“Singular General Model of 2-D Systems and its Solutions” IEEE Transactions on Automatic Controls. 33 1061–1091
T. Kaczorek (1990) ArticleTitle“General Response Formula and Minimums Energy Control for the General Singular Model for 2-D systems” IEEE Transactions on Automatic Control. 35 433–436
AV. Karamanciogle FL. Lewis (1992) ArticleTitle“Geometric Theory for Singular Roesser Model” IEEE Transactions on Automatic Control. 37 801–806
T. Kaczorek (1993) ArticleTitle“Acceptable Input Sequences for Singular 2-D Linear Systems” IEEE Transactions on Automatic Control. 38 1391–1394
Y. Zou SL. Campbell (2000) ArticleTitle“The Jump Behavior and Stability Analysis for 2-D Singular Systems” Multidimensional Systems and Signal Processing. 11 321–338
C. Cai W. Wang Y. Zou (2004) ArticleTitle“A Note on the Internal Stability for 2-D Acceptable Linear Singular Discrete Systems” Multidimensional Systems and Signal Processing. 15 197–204
Zou Y., Wang W., Xu S. “Structural Stability of 2-D Singular Systems-Part I: Basic Properties”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, 2003
Zou Y., Wang W., Xu S. “Structural Stability of 2-D Singular Systems Part II: A Lyapunov Approach”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, (2003)
W. Wang Y. Zou (2002) ArticleTitle“The Detectability and Observer Design of 2-D Singular Systems” IEEE Transactions Circuits and Systems. 49 IssueID5 698–703 Occurrence HandleMR1909321
Zou Y., Wang W., Xu S. “Regular State Observers Design for 2-D Singular Roesser Models”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, 2003
T. Kaczorek (1989) ArticleTitle“The Linear-quadratic Optimal Regulator for Singular 2-D Systems with Variable Coefficients” IEEE Transactions on Automatic Control. 34 565–566
H. Xu Y. Zou S. Xu J. Lam (2005) ArticleTitle“Bounded Real Lemma and Robust H∞ Control of 2-D Singular Roesser Models” Systems and ontrol Letters. 54 339–346
T. Iwasaki RE. Skelton (1994) ArticleTitle“All Controllers for the General H∞ Control Problem: LMI Existence Conditions and State Space Formulas” Automatica. 30 IssueID8 1307–1317
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xu, H., Zou, Y., Xu, S. et al. H∞ Model Reduction of 2-D Singular Roesser Models. Multidim Syst Sign Process 16, 285–304 (2005). https://doi.org/10.1007/s11045-005-1678-1
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11045-005-1678-1