Delay-dependent robust stabilisation of discrete-time systems with time-varying delay

Author(s): X.G. Liu ; R.R. Martin ; M. Wu ; M.L. Tang
DOI: 10.1049/ip-cta:20050223

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Author(s): X.G. Liu ^{1, 2, 3} ; R.R. Martin ² ; M. Wu ³ ; M.L. Tang ¹
- Affiliations: 1: School of Mathematical Science and Computing Technology, Central South University, Changsha, People's Republic of China
  2: School of Computer Science, Cardiff University, Cardiff, UK
  3: School of Information Science and Engineering, Central South University, Changsha, People's Republic of China
Source: Volume 153, Issue 6, November 2006, p. 689 – 702
DOI: 10.1049/ip-cta:20050223 , Print ISSN 1350-2379, Online ISSN 1359-7035

The stability of discrete systems with time-varying delay is considered. New delay-dependent stability criteria are devised, which are dependent on the minimum and maximum delay bounds. An initial analysis leads to a criterion depending on an inequality involving certain matrices that can be freely chosen. By carefully choosing them to reflect the appropriate relationship between states at differing times, a stricter criterion is thereby obtained. Furthermore, new results for delay-dependent robust stabilisation of uncertain systems with time-varying delay are provided on the basis of a linear matrix inequality (LMI) framework. As the conditions obtained for the existence of admissible controllers are not expressed using strict LMI conditions, a cone complementary linearisation procedure is used to find suitable controllers. Finally, the results obtained, including the stability analysis, static output-feedback stabilisation and dynamic output feedback stabilisation are further extended to discrete time-delay systems having uncertain but norm-bounded parameters. Numerical examples demonstrate the validity of the approach proposed.

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Delay-dependent robust stabilisation of discrete-time systems with time-varying delay

Delay-dependent robust stabilisation of discrete-time systems with time-varying delay

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