caa a22 4500 606199217 CHVBK 20210128100937.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s11045-013-0237-4 doi (NATIONALLICENCE)springer-10.1007/s11045-013-0237-4 A frequency-partitioning approach to stability analysis of two-dimensional discrete systems [Elektronische Daten] [Xianwei Li, James Lam, Huijun Gao, Yue Gu] Although there exist necessary and sufficient conditions for two-dimensional (2-D) discrete systems, their application scope is almost limited to system analysis only and no work has demonstrated their possible extension to system synthesis. In this paper, we propose a novel frequency-partitioning approach to analyzing stability of 2-D discrete state-space systems. A piecewise constant matrix function is introduced to approximate the solution to the frequency-dependent Lyapunov inequality, whose solvability is known to be equivalent to stability of a 2-D state-space model. Then by the generalized Kalman-Yakubovich-Popov Lemma, new stability conditions are derived for the Roesser model and the Fornasini-Marchesini (FM) first and second models, respectively. Stability criteria in the paper simultaneously overcome the drawbacks of the simple 2-D Lyapunov inequality approach and the existing necessary and sufficient conditions: (1) They are expressed in terms of linear matrix inequalities (LMIs), which are generally less conservative than the existing simple 2-D Lyapunov inequality-based results, and could be improved by increasing the partitioning number; (2) Since each of the LMIs corresponds to a simple 2-D Lyapunov inequality, they are more suitable for further development for system synthesis than the existing necessary and sufficient conditions, which is demonstrated by an illustrative application to state-feedback control of an uncertain FM second model. Springer Science+Business Media New York, 2013 Stability nationallicence Two-dimensional (2-D) systems nationallicence State-space models nationallicence Frequency-partitioning nationallicence Lyapunov inequality nationallicence Li Xianwei Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, 150080, Harbin, Heilongjiang Province, People's Republic of China aut Lam James Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People's Republic of China aut Gao Huijun Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, 150080, Harbin, Heilongjiang Province, People's Republic of China aut Gu Yue Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai Institute of Spaceflight Control Technology, 200233, Shanghai, People's Republic of China aut Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/1(2015-01-01), 67-93 0923-6082 26:1<67 2015 26 11045 https://doi.org/10.1007/s11045-013-0237-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11045-013-0237-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Xianwei Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, 150080, Harbin, Heilongjiang Province, People's Republic of China aut NATIONALLICENCE 700 1- Lam James Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People's Republic of China aut NATIONALLICENCE 700 1- Gao Huijun Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, 150080, Harbin, Heilongjiang Province, People's Republic of China aut NATIONALLICENCE 700 1- Gu Yue Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai Institute of Spaceflight Control Technology, 200233, Shanghai, People's Republic of China aut NATIONALLICENCE 773 0- Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/1(2015-01-01), 67-93 0923-6082 26:1<67 2015 26 11045