State feedback stabilization of nonlinear discrete-time systems with time-varying time delay

Abstract This paper deals with the class of nonlinear discrete-time systems with varying time delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper bound and a lower bound on the time-varying delay, sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided for determining the state feedback controller gain. All the results developed in this paper are in the LMI formalism which makes it easier to obtain them using existing tools. A numerical example is provided to show the effectiveness of the results established.

[1]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[2]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

[3]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[4]  Jong Hae Kim,et al.  Hinfinity state feedback control for generalized continuous/discrete time-delay system , 1999, Autom..

[5]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[6]  S. Su,et al.  LMI approach to static output feedback simultaneous stabilization of discrete-time interval systems with time delay , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[7]  Hiroaki Mukaidani,et al.  LMI-based neurocontroller for guaranteed cost control of uncertain time-delay systems , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[8]  E. Boukas,et al.  Robust stability and H/sub /spl infin// control of discrete-time jump linear systems with time-delay: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  Seong-Ho Song,et al.  H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state , 1998, Autom..

[10]  El-Kébir Boukas,et al.  H/sub /spl infin// control for discrete-time linear systems with Markovian jumping parameters , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.