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http://dx.doi.org/10.5370/KIEE.2013.62.4.529

Delay-dependent Robust Stability of Discrete-time Uncertain Delayed Descriptor Systems using Quantization/overflow Nonlinearities  

Kim, Jong-Hae (Dept. of Electronic Engineering, Sun Moon University)
Oh, Do-Cang (Dept. of Biomedical Engineering, Konyang University)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.62, no.4, 2013 , pp. 529-535 More about this Journal
Abstract
This paper considers the problem of robust stability for uncertain discrete-time interval time-varying delayed descriptor systems using any combinations of quantization and overflow nonlinearities. First, delay-dependent linear matrix inequality (LMI) condition for discrete-time descriptor systems with time-varying delay and quantization/overflow nonlinearities is presented by proper Lyapunov function. Second, it is shown that the obtained condition can be extended into descriptor systems with uncertainties such as norm-bounded parameter uncertainties and polytopic uncertainties by some useful lemmas. The proposed results can be applied to both descriptor systems and non-descriptor systems. Finally, numerical examples are shown to illustrate the effectiveness and less conservativeness.
Keywords
Nonlinear descriptor systems; Robust stability; Finite wordlength effect; Uncertain descriptor systems; Time-varying delay; LMI;
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1 L. J. Leclerc and P. H. Bauer, "New Criteria for asymptotic stability of one- and multi dimensional state-space digital filters in fixed-point arithmetic," IEEE Transactions on Signal Processing, vol. 42, no. 1, pp. 46-53, 1994.   DOI   ScienceOn
2 H. Kar and V. Singh, "Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities," IEEE Transactions on Signal Processing, vol. 49, no. 5, pp. 1097-1105.
3 H. Kar and V. Singh, "Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities," IEEE Transactions on Circuits and Systems II, vol. 51, no. 11, pp. 598-602, 2004.
4 H. Kar, "A new sufficient condition for the global asymptotic stability of 2-D state-space digital filters with saturation arithmetic," Signal Processing, vol. 88, no. 1, pp. 86-98, 2008.   DOI   ScienceOn
5 H. Kar, "An improved version of modified Liu-Michel's criterion for global asymptotic stability of fixed-point state-space digital filters using saturation arithmetic," Digital Signal Processing, vol. 20, no. 4, pp. 977-981, 2010.   DOI   ScienceOn
6 V. K. R. Kandanvli and H. Kar, "Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach," Signal Processing, vol. 89, no. 2, pp. 161-173, 2009.   DOI   ScienceOn
7 V. K. R. Kandanvli and H. Kar, "An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities," Signal Processing, vol. 89, no. 11, pp. 2092-2102, 2009.   DOI   ScienceOn
8 V. K. R. Kandanvli and H. Kar, "Delay-dependent LMI condition for global asymptotic stability of discrete-time uncertain state-delayed systems using quantization/overflow nonlinearities," International Journal of Robust and Nonlinear Control, vol. 21, no. 14, pp. 1611-1622, 2011.   DOI   ScienceOn
9 E. K. Boukas, Control of Singular Systems with Random Abrupt Changes, Springer-Verlag Berlin, Heidelberg, 2008.
10 W. Li, E. Todorov and R. E. Skelton, "Estimation and control of systems with multiplicative noise via linear matrix inequalities," American Control Conference, Portland, OR, USA, pp. 1811-1816, 2005.
11 S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
12 X. M. Zhang and Q. L. Han, "Delay-dependent robust $H_{{\infty}}$ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality," IEEE Transactions on Circuits and Systems II, Express Briefs, vol. 53, no. 12, pp. 1466-1470, 2006.   DOI   ScienceOn
13 P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox, MA, The Mathworks Inc. 1995.