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Original Articles

A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays

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Pages 845-853 | Received 22 Jan 2010, Accepted 30 Aug 2010, Published online: 23 Nov 2010

References

  • Cho , HC , Lee , KS and Fadali , MS . 2009 . Adaptive Control of PMSM Systems with Chaotic Nature Using Lyapunov Stability Based Feedback Linearization . International Journal of Innovative Computing, Information and Control , 5 : 479 – 488 .
  • Dashkovskiy, S., Görges, M., and Naujok, L. (2009), ‘Local Input to State Stability of Production Networks’, in Proceedings of the Second International Conference on Dynamics in Logistics, LDIC 2009, Bremen, Germany, August 2009.
  • Dashkovskiy, S., and Naujok, L. (2010), ‘Lyapunov–Razumikhin and Lyapunov–Krasovskii Theorems for Interconnected ISS Time-delay Systems’, in Proceedings of the MTNS 2010, Budapest, Hungary, July 05–09.
  • Dashkovskiy , SN and Rüffer , BS . 2010 . Local ISS of Large-scale Interconnections and Estimates for Stability Regions . Systems & Control Letters , 59 : 241 – 247 .
  • Dashkovskiy , S , Rüffer , B and Wirth , F . 2007 . An ISS Small-gain Theorem for General Networks . Mathematics Control Signals Systems , 19 : 93 – 122 .
  • Dashkovskiy , SN , Rüffer , BS and Wirth , FR . 2010 . Small Gain Theorems for Large-scale Systems and Construction of ISS Lyapunov Functions . SIAM Journal on Control and Optimization , 48 : 4089 – 4118 .
  • Esfanjani, R.M., Reble, M., Münz, U., Kamaleddin, S., Nikravesh, Y., and Allgöwer, F. (2009), ‘Model Predictive Control of Constrained Nonlinear Time-delay Systems’, in Proceedings of CDC/CCC 2009, The Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, December 16–18, 2009.
  • Hou , C and Qian , J . 1998 . On an Estimate of the Decay Rate for Applications of Razumikhin-type Theorems . IEEE Transactions on Automatic Control , 43 : 958 – 960 .
  • Ignaciuk, P., and Bartoszewicz, A. (2009), ‘LQ Optimal Inventory Control for Multi-supplier Periodic-review Systems with Disparate Lead-time Delay’, in Proceedings of CDC/CCC 2009, The Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, December 16–18, 2009.
  • Jiang , Z-P , Mareels , IMY and Wang , Y . 1996 . A Lyapunov Formulation of the Nonlinear Small-gain Theorem for Interconnected ISS Systems . Automatica Journal of IFAC , 32 : 1211 – 1215 .
  • Karafyllis, I., and Jiang, Z.-P. (2009), ‘A Vector Small-gain Theorem for General Nonlinear Control Systems’, http://arxiv.org/pdf/0904.0755
  • Khalil , HK . 1996 . Nonlinear Systems , Upper Saddle River , NJ : Prentice Hall .
  • Li , H , Chen , B , Zhou , Q and Su , Y . 2010 . New Results on Delay-dependent Robust Stability of Uncertain Time Delay Systems . International Journal of Systems Science , 41 : 627 – 634 .
  • Niculescu , S-I and Gu , K . 2004 . Advances in Time-delay Systems , New York : Springer .
  • Shi , P . 1998 . Robust Control of Linear Continuous Time-delay Systems with Finite Discrete Jumps and Norm-bounded Uncertainties . International Journal of Systems Science , 29 : 1381 – 1392 .
  • Silva , CA , Sousa , JMC , Runkler , TA and Sa da Costa , JMG . 2006 . Distributed Optimisation of a Logistic System and Its Suppliers using Ant Colonies . International Journal of Systems Science , 37 : 503 – 512 .
  • Song , W , Wang , D , Li , H and Wang , W . 2010 . Stability Analysis of a Class of Nonlinear Dynamic Systems . ICIC Express Letters , 4 : 281 – 288 .
  • Sontag , ED . 1989 . Smooth Stabilization Implies Coprime Factorization . IEEE Transaction on Automatic Control , 34 : 435 – 443 .
  • Sontag , ED and Wang , Y . 1996 . New Characterizations of Input-to-state Stability . IEEE Transactions on Automatic Control , 41 : 1283 – 1294 .
  • Tai , Z , Wang , X , Li , H and Wang , W . 2010 . Stability Analysis of Nonlinear Neutral Functional Differential Equations . ICIC Express Letters , 4 : 125 – 130 .
  • Teel , AR . 1998 . Connections Between Razumikhin-type Theorems and the ISS Nonlinear Small Gain Theorem . IEEE Transaction on Automatic Control , 43 : 960 – 964 .
  • Tiwari, S., Wang, Y., and Jiang, Z.-P. (2009), ‘A Nonlinear Small-gain Theorem for Large-scale Time Delay Systems’, in Proceedings of CDC/CCC 2009, The Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, December 16–18, 2009.
  • Wang , Q , Lam , J , Xu , S and Gao , H . 2005 . Delay-dependent and Delay-independent Energy-to-peak Model Approximation for Systems with Time-varying Delay . International Journal of Systems Science , 36 : 445 – 460 .
  • Wang , Z and Gao , H . 2009 . Analysis and Synchronization of Complex Networks . International Journal of Systems Science , 40 : 905 – 907 .
  • Wu , Y . 2008 . A Mixed-integer Programming Model for Global Logistics Transportation Problems . International Journal of Systems Science , 39 : 217 – 228 .
  • Xia , Y , Liu , GP , Shi , P , Rees , D and Thomas , EJC . 2007 . New Stability and Stabilization Conditions for Systems with Time-delay . International Journal of Systems Science , 38 : 17 – 24 .
  • Yoneyama , J and Tsuchiya , T . 2008 . New Delay-dependent Conditions on Robust Stability and Stabilisation for Discrete-time Systems with Time-delay . International Journal of Systems Science , 39 : 1033 – 1040 .
  • Zhai , G , Matsune , I , Imae , J and Kobayashi , T . 2009 . A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems . International Journal of Innovative Computing, Information and Control , 5 : 1189 – 1200 .

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