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

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4 Author(s)
Liu, X.G. ; Sch. of Math. Sci. & Comput. Technol., Central South Univ., Changsha ; Martin, R.R. ; Wu, M. ; Tang, M.L.

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

Published in:

Control Theory and Applications, IEE Proceedings  (Volume:153 ,  Issue: 6 )