Vietnam Journal of Mathematics

, Volume 43, Issue 2, pp 215–228 | Cite as

State Feedback Guaranteed Cost Controller for Nonlinear Time-Varying Delay Systems

  • Piyapong Niamsup
  • Vu Ngoc PhatEmail author


This paper considers the problem of designing state feedback guaranteed cost controllers for a class of nonlinear systems with time-varying delay. The time delay is a continuous function belonging to a given interval and not required to be differentiable. By applying Lyapunov function method and linear matrix inequality (LMI) technique, new delay-dependent sufficient conditions for designing the state feedback guaranteed cost controller are derived. The method is also extended to handle system uncertainties in a straightforward way. A numerical example is given to illustrate the design procedure.


Guaranteed cost control Stabilization Interval time-varying delays Lyapunov function Linear matrix inequalities 

Mathematics Subject Classification (2010)

93D20 34D20 37C75 



This work is supported by the National Foundation for Science and Technology Development, Vietnam under grant 101.01.2014.35 and the Chiang Mai University, Thailand. The authors would like to thank anonymous reviewer for valuable comments, which have improved our paper.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand
  2. 2.Institute of MathematicsVASTHanoiVietnam

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