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

2007 ◽  
Vol 66 (6) ◽  
pp. 1341-1350 ◽  
Author(s):  
E.K. Boukas
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
State Feedback ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Varying Time Delay ◽  
Time Systems

scholarly journals Discrete-time systems with time-varying time delay: Stability and stabilizability

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
El-Kébir Boukas
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Design Algorithm ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Varying Time Delay ◽  
The Stability ◽  
Time Systems

This paper deals with the class of linear 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. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.

Delay-Dependent Stabilization of Discrete-Time Systems With Time-Varying Delay via Switching Technique

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Hui Zhang ◽  
Yang Shi
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Time Varying ◽  
Design Algorithm ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Measured Time ◽  
Sampling Instant ◽  
Delay Dependent ◽  
Time Systems

In this paper, we investigate the stabilization problem of time-delay discrete-time systems with occurrence probabilities for time delays. Using an augmenting technique, we convert random time-delay discrete-time systems to delay-free systems with stochastic variables. We propose to design a sequence of delay-dependent controllers. The implemented controller is chosen according to the measured time delay at each sampling instant. When the delay is randomly time-varying, the implemented controller is switched in a designed controller set. An example is provided to illustrate the effectiveness of the stability condition and another example is offered to show the applicability of the proposed design algorithm.

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