Acta Mathematica Vietnamica

, Volume 41, Issue 3, pp 481–493

Finite-Time Stability and H Control of Linear Discrete-Time Delay Systems with Norm-Bounded Disturbances


DOI: 10.1007/s40306-015-0155-7

Cite this article as:
Tuan, L.A. & Phat, V.N. Acta Math Vietnam (2016) 41: 481. doi:10.1007/s40306-015-0155-7


This paper deals with the finite-time stability and H control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First, new sufficient conditions are established for robust finite-time stability of the linear discrete-time delay system with norm-bounded disturbances, then the state feedback controller is designed to robustly finite-time stabilize the system and guarantee an adequate level of system performance. The delay-dependent sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed results.


Finite-time stability H control Time-varying delay Disturbances Linear matrix inequalities 

Mathematics Subject Classification (2010)

34D10 34K20 49M7 

Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesHue UniversityHueVietnam
  2. 2.Institute of Mathematics, VASTHanoiVietnam

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