Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31181
Reachable Set Bounding Estimation for Distributed Delay Systems with Disturbances

Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: distributed delay, Reachable set, Lyapunov-Krasovskii function, Polytopic uncertainties

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1097134

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1492

References:


[1] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnam, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, PA, 1994.
[2] Boyd S,Ghaoui LE, Feron E, Balakrishnan V. Linear matrix inequalities in system and control theory. Society for Industrial an Applied Mathematics, PA:Philadelphia 1994.
[3] S. Boyd, Lecture Notes for Convex Optimization II, 2007.¡http://www.stanford.edu/class/ee364b/lectures.html¿
[4] Q.L. Han, on robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica 40 (2004) 1087-1092.
[5] J.H. Kim, Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances, Automatica 44 (2008) 2940-2943
[6] Z. Zuo, D.W.C. Ho, Y. Wang, Reachable set bounding for delayed systems with polytopic uncertainties: the maximal LyapunovCKrasovskii functional approach, Automatica 46 (2010) 949-952
[7] Z. Zuo, D.W.C. Ho, Y.Wang, Reachable set estimation for linear systems in the presence of both discrete and distributed delays, IET Control Theory Appl. 5 (15) (2011) 1808-1812.
[8] Z.Zuo,C.Yang,Y Wang,A new method for stability analysis of recurrent neural networks with interval time-varying delay,IEEE Trans.Neural Networks 21(2)(2010)339-344.
[9] D. Zhang, L. Yu, H∞ filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations, Journal of the Franklin Institute 347 (2010) 1374-1390.
[10] C. Shen, S. Zhong, The ellipsoidal bound of reachable sets for linear neutral systems with disturbances, J. Frankl. Inst. 348 (2011) 2570-2585
[11] E. Fridman, U. Shaked, On reachable sets for linear systems with delay and bounded peak inputs, Automatica 39 (2003) 2005-2010.
[12] A. Alessandri, M. Baglietto, G. Battistelli, On estimation error bounds for receding-horizon filters using quadratic boundedness, IEEE Transactions on Automatic Control 49 (2004) 1350-1355.
[13] O.M. Kwon, S.M. Lee, Ju H. Park, On reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances, Inf. Sci. 181 (2011) 3735-3748.
[14] A. Alessandri, M. Baglietto, G. Battistelli, Design of state estimators for uncertain linear systems using quadratic boundedness, Automatica 42 (2006) 497-502.
[15] Y.H.Du,S.M.Zhong,Exponential passivity of BAM neural networks with time-varying delays.Applied Mathematics and Computation 221(2013)727-740.
[16] Y. He, Q.G. Wang, L.H. Xie, C. Lin, Further improvement of freeweighting matrices technique for systems with time-varying delay, IEEE Transactions on Automatic Control 52 (2) (2007) 293-299.
[17] P.T. Nam, P.N. Pathirana, Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays, Automatica 47 (2011) 1838-1841
[18] N. Ramdani, N. Meslem, Y. Candau, A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems, IEEE Transactions on Automatic Control 54 (10) (2009) 2352-2364