# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model. (English) Zbl 1197.34133
Summary: This paper addresses the problem of delay-dependent stability of 2D systems with time-varying delay subject to state saturation in the Roesser model. By introducing diagonally dominant matrices, new delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs) where the lower and upper delay bounds along horizontal and vertical directions, respectively, are known. Numerical examples are provided to demonstrate the proposed results.
##### MSC:
 34K20 Stability theory of functional-differential equations
##### References:
 [1] Du, C.; Xie, L.; Zhang, C.: Control and filtering of two-dimensional systems, (2002) [2] Kaczorek, T.: Two-dimensional linear systems, (1985) [3] Lu, W. S.: Two-dimensional digital filters, (1992) [4] Liu, D.; Michel, A. N.: Dynamical systems with saturation nonlinearities, (1994) [5] Liu, D.; Michel, A. N.: Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities, IEEE trans. Circuits syst. – I 41, 127-137 (1994) · Zbl 0845.93072 · doi:10.1109/81.269049 [6] Kar, H.; Singh, V.: Stability analysis of 1D and 2D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities, IEEE trans. Signal process. 49, 1097-1105 (2001) [7] Kar, H.; Singh, V.: Stability analysis of 2D digital filters with saturation arithmetic: an LMI approach, IEEE trans. Signal process. 53, 2267-2271 (2005) [8] Kar, H.: A new sufficient condition for the global asymptotic stability of 2D state-space digital filters with saturation arithmetic, Signal process. 88, 86-98 (2008) · Zbl 1186.94169 · doi:10.1016/j.sigpro.2007.07.005 [9] Singh, V.: Robust stability of 2D digital filters employing saturation, IEEE signal process. Lett. 12, 142-145 (2005) [10] Singh, V.: Elimination of overflow oscillations in 2D digital filters employing saturation arithmetic: an LMI approach, IEEE signal process. Lett. 12, 246-249 (2005) [11] Singh, V.: Improved criterion for global asymptotic stability of 2D discrete systems with sate saturation, IEEE signal process. Lett. 14, 719-722 (2007) [12] Singh, V.: New LMI condition for the nonexistence of overflow oscillations in 2D state-space digital filters using saturation arithmetic, Digit. signal process. 17, 345-352 (2007) [13] Singh, V.: On global asymptotic stability of 2D discrete systems with sate saturation, Phys. lett. A 372, 5287-5289 (2008) · Zbl 1223.93054 · doi:10.1016/j.physleta.2008.06.009 [14] Chen, S. -F.; Fong, I. K.: Robust filtering for 2D state-delayed systems with NFT uncertainties, IEEE trans. Signal process. 54, 274-285 (2006) [15] Chen, S. -F.; Fong, I. K.: Delay-dependent robust H$\infty$ filtering for uncertain 2D state-delayed systems, Signal process. 87, 2659-2672 (2007) · Zbl 1186.94088 · doi:10.1016/j.sigpro.2007.04.015 [16] Peng, D.; Guan, X.: Output feedback H$\infty$ control for 2D state-delayed systems, Circuits syst. Signal process. 28, 147-167 (2009) · Zbl 1163.93331 · doi:10.1007/s00034-008-9074-3 [17] Peng, D.; Guan, X.: H$\infty$ filtering for 2D state-delayed systems, Multi-dimensional syst. Signal process. 20, 265-284 (2009) · Zbl 1169.93363 · doi:10.1007/s11045-008-0064-1 [18] Paszke, W.; Lam, J.; Gałkowski, K.; Xu, S.; Lin, Z.: Robust stability and stabilization of 2D discrete state-delayed systems, Syst. contr. Lett. 51, 277-291 (2004) · Zbl 1157.93472 · doi:10.1016/j.sysconle.2003.09.003 [19] Ye, S.; Wang, W.; Zou, Y.: Robust guaranteed cost control for class of two-dimensional discrete systems with shift-delays, Multi-dimensional syst. Signal process. 20, 297-307 (2009) · Zbl 1169.93336 · doi:10.1007/s11045-008-0063-2 [20] Gao, H.; Chen, T.: New results on stability of discrete-time systems with time-varying state delay, IEEE trans. Automat. control 52, 328-333 (2007) [21] He, Y.; Wu, M.; Liu, G. -P.; She, J. -H.: Output feedback stabilization for a discrete-time system with a time-varying delay, IEEE trans. Automat. control 53, 2372-2377 (2008) [22] Qiu, J.; Xia, Y.; Yang, H.; Zhang, J.: Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators, IET control theor. Appl. 2, 87-93 (2008) [23] Kandanvli, V. K. R.; Kar, H.: Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities, Nonlinear anal. – theor. 69, 2780-2787 (2008) · Zbl 1147.93035 · doi:10.1016/j.na.2007.08.050 [24] Kandanvli, V. K. R.; Kar, H.: Robust stability of discrete-time state-delayed systems with saturation nonlinearities: linear matrix inequality approach, Signal process. 89, 161-173 (2009) · Zbl 1155.94325 · doi:10.1016/j.sigpro.2008.07.020 [25] Chen, S. -F.: Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities, Chaos solitions fractals 42, 1251-1257 (2009) · Zbl 1198.93193 · doi:10.1016/j.chaos.2009.03.026 [26] Roesser, R. P.: A discrete state-space model for linear image processing, IEEE trans.automat. Control 20, 1-10 (1975) · Zbl 0304.68099 · doi:10.1109/TAC.1975.1100844 [27] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994) [28] Gao, H.; Lames, J.; Wang, C.: Induced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities, IEEE trans. Signal process. 53, 4215-4226 (2005) [29] Chu, Y. C.; Glover, K.: Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities, IEEE trans. Automat. control 44, 471-478 (1999) · Zbl 0958.93059 · doi:10.1109/9.751342 [30] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M.: LMI control toolbox for use with Matlab, (1995)