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.

scholarly journals Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Jiemei Zhao ◽  
Yin Sheng
Keyword(s):  
Discrete Time ◽  
Reachable Set ◽  
Time Varying ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Discrete Time Systems ◽  
Bounded Disturbances ◽  
Reachable Set Estimation ◽  
Time Systems ◽  
Varying Delay

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

scholarly journals New stability conditions for a class of nonlinear discrete-time systems with time-varying delay

2021 ◽  
Author(s):  
SAMI ELMADSSIA ◽  
KARIM SADAAOUI
Keyword(s):  
Discrete Time ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Matrix Properties ◽  
Arrow Form Matrix ◽  
Bounded Nonlinearity ◽  
Time Systems ◽  
Varying Delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

scholarly journals Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Priyanka Kokil ◽  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results.

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