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.

scholarly journals Stability Analysis of Linear Discrete-Time Systems with Interval Delay: A Delay-Partitioning Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Priyanka Kokil ◽  
Haranath Kar ◽  
V. Krishna Rao Kandanvli
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Partition Size ◽  
New Criterion ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This paper considers the problem of asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By using a delay partitioning-based Lyapunov functional, a new criterion for the asymptotic stability of such systems is proposed in terms of linear matrix inequalities (LMIs). The proposed stability condition depends on both the size of delay and partition size. The presented approach is compared with previously reported approaches.

scholarly journals A Novel Wirtinger-Based Inequality to H∞ Filtering for Discrete-Time Systems with Time-Varying Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Kaifan Ma ◽  
Zhangang Wang ◽  
Fengdong Shi ◽  
Liankun Sun
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This article is committed to H∞ filtering for linear discrete-time systems with time-varying delay. The novelty of the paper comes from the consideration of the new Wirtinger-based inequality with double accumulation terms and the idea of delay-partitioning, which guarantees a better asymptotic stability and is less conservative than the celebrated free-weighting matrix or Jensen’s inequality methods. In combination with the improved Wirtinger-based inequality to handle the modified Lyapunov-Krasovskii (L-K) functionals, a new delay-dependent bound real lemma (BRL) is gained. In the light of the derived H∞ performance analysis results, the H∞ filter will be designed in response to linear matrix inequality (LMI). The validness of the proposed methods will be expressed via some numerical examples by the comparison of existing results.

scholarly journals Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Valter J. S. Leite ◽  
Márcio F. Miranda
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Robust Stability Analysis ◽  
Time Systems ◽  
Varying Delay

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

Delay-Partitioning Approach to H∞ Performance Analysis of Discrete-Time Systems with Interval Time-Varying Delay

2013 ◽  
Vol 427-429 ◽  
pp. 1364-1367 ◽  
Author(s):  
Li Lee ◽  
Hsing Jen Tsai
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
Jensen Inequality ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Partition Approach ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

The paper addresses performance analysis of discrete-time systems with time-varying delay of value bounded in a known interval. A set of sufficient LMI conditions is obtained from using the Jensen inequality to ensure asymptotical stability and-norm bounded by a specified value. The delay partition technique is exploited further to reduce the conservativeness induced by the Jensen inequality treatment. Simulation results show the benefit of the used delay partition approach.

scholarly journals Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Guangdeng Zong ◽  
Linlin Hou ◽  
Hongyong Yang
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Varying Delay

This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

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>

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