New results on convergence of fuzzy cellular neural networks with multi-proportional delays

Gang Yang1
1School of Mathematics and Statistics, Hunan University of Commerce, Changsha, People’s Republic of China

Tóm tắt

In this paper, we propose and study the global exponential convergence of a class of fuzzy cellular neural networks with multi-proportional delays, which has not been studied in the existing literature. Applying the differential inequality technique and Lyapunov functional method, we establish a set of global exponential convergence criteria. The sufficient criteria can be easily tested in practice by simple algebra computations. The obtained results play an important role in designing fuzzy neural networks. Moreover, an illustrative example is given to demonstrate our theoretical results.

Tài liệu tham khảo

Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proceeding 1990 IEEE Int. Workshop on cellular neural networks and their applications, pp 12–25 Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302 Zhang A (2015) New results on exponential convergence for cellular neural networks with continuously distributed leakage delays. Neural Process Lett 41:421–433 Kwon O, Park J (2009) Exponential stability analysis for uncertain neural networks with interval time-varying delays. Appl Math Comput 212:530–541 Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, Belin Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256 Wu X, Wang Y, Huang L, Zuo Y (2010) Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays. Neurocomputing 73:1265–1271 Liao X, Chen G, Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 49(7):1033–1039 Xiao J, Zhong S, Li Y (2016) Relaxed dissipativity criteria for memristive neural networks with leakage and time-varying delays. Neurocomputing 171:708–718 Xiao J, Zhong S, Li Y (2015) New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays. ISA T 59:133–148 Xiao J, Zhong S, Li Y (2016) Improved passivity criteria for memristive neural networks with interval multiple time-varying delays. Neurocomputing 171:1414–1430 Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 181–186 Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 225–230 Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111 Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138 Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80 Zheng C, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17 Kao Y, Shi L, Xie J, Karimi HR (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30 Song X, Zhao P, Xing Z, Peng J (2016) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Methods Appl Sci 39:722–733 Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120 Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163 Zhou L (2013) Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359 Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682 Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161:99–106 Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355 Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc Lond Ser A Math PhysEng Sci 322:447–468 Fox L, Mayers DF, Ockendon JR, Tayler AB (1971) On a functional-differential equation. J Inst Math Appl 8(3):271–307 Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci 39:4520–4525 Liu B (2016) Global exponential convergence of non-autonomous SICNNs with multi-proportional delays. Neural Comput Appl. doi:10.1007/s00521-015-2165-8 Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{\rm {o}}\)dinger operators. Oper Theory Adv Appl 46:319–321 Huang Z (2016) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl. doi:10.1007/s00521-016-2194-y Huang Z (2016) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cyber doi:10.1007/s13042-016-0507-1