Predictor-based stabilization of discrete time-varying input-delay systems

Automatica ◽  
2012 ◽  
Vol 48 (2) ◽  
pp. 454-457 ◽  
Author(s):  
A. Gonzalez ◽  
A. Sala ◽  
P. Albertos
Keyword(s):  
Discrete Time ◽  
Input Delay ◽  
Delay Systems ◽  
Time Varying

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

scholarly journals H∞ Control of Discrete-time Input-delay Systems with Observer-based Prediction

2016 ◽  
Vol 49 (8) ◽  
pp. 150-155
Author(s):  
Kotaro Hashikura ◽  
Akira Kojima
Keyword(s):  
Discrete Time ◽  
Input Delay ◽  
Delay Systems

scholarly journals New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1531 ◽  
Author(s):  
Sami Elmadssia ◽  
Karim Saadaoui
Keyword(s):  
Discrete Time ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Aggregation Techniques ◽  
Discrete Time Delay ◽  
Time Systems ◽  
Varying Delay

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. 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 nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

scholarly journals Robustl2-l∞Filtering for Discrete-Time Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengming Yang ◽  
Zhandong Yu ◽  
Pinchao Wang ◽  
Zhen Yu ◽  
Hamid Reza Karimi ◽  
...  
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Estimation Error ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Discrete Time Delay ◽  
Error System ◽  
Varying Delay

The problem of robustl2-l∞filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on thel2-l∞performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficientl2-l∞performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robustl2-l∞filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.

A SWITCHING RULE FOR THE ASYMPTOTIC STABILITY OF UNCERTAIN DISCRETE-TIME SYSTEMS

2011 ◽  
Vol 08 (03) ◽  
pp. 255-261 ◽  
Author(s):  
K. RATCHAGIT
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Uncertain System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Switching Rule ◽  
Discrete Time Delay ◽  
Time Systems

This paper is concerned with asymptotic stability of uncertain switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability for the uncertain system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

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