A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays
Two recent Lyapunov-based methods: delay-partitioning approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one-dimensional (1-D) time-delay systems, respectively. This paper concerns the analysis of delay-dependent stability for two-dimensional (2-D) discrete systems with interval time-varying delays. By applying a delay partitioning-based Lyapunov function combining with the approaches of 2-D Jensen inequalities, a new delay-dependent stability criterion is derived in terms of linear matrix inequality (LMI). In addition to delay dependence, the obtained criterion is also dependent on the partition size. It is rigorously proved that the authors’ result reduces the conservativeness and computational burden than some recent ones. Numerical examples show the effectiveness and advantage of our result.
KeywordsDelay-partitioning approach delay-dependent interval time-varying delays linear matrix inequality (LMI) two-dimensional (2-D) discrete systems 2-D Jensen inequalities
Unable to display preview. Download preview PDF.
- S. X. Ye and J. Z. Li, “Robust control for a class of 2-D discrete uncertain delayed systems,” Proc. of 10th IEEE International Conference on Control and Automation (ICCA), Hangzhou, China, pp. 1048–1052, June 12-14, 2013. [click]Google Scholar
- S. K. Tadepalli, V. K. R. Kandanvli, and H. Kar, “A new delay-dependent stability criterion for uncertain 2-D discrete systems described by Roesser model under the influence of quantization/overflow nonlinearities,” Circuits, Systems, and Signal Processing, vol. 34, no. 8, pp. 2537–2559, August 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
- X. L. Zhu and G. H. Yang, “Jensen inequality approach to stability analysis of discrete-time systems with timevarying delay,” Proc. of American Control Conference, Washington, USA, pp. 1644–1649, June 11-13, 2008.Google Scholar
- Q. Li, Y. T. Wang, H. Y. Zhu, and Y. M. Hu, “Delaypartition- dependent robust stability criteria for uncertain discrete-time systems with an interval time-varying state delay,” Lecture Notes in Electrical Engineering, vol. 121, no. 121, pp. 557–564, 2012. [click]Google Scholar
- P. Kokil, H. Kar, and V. Kandanvli, “Stability analysis of linear discrete-time systems with interval delay: a delaypartitioning approach,” ISRN Applied Mathematics, vol. 2011, no. 2, October 2011. [click]Google Scholar