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.

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 Efficient Approach to Stability Analysis of Discrete-Time Systems with Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Sung Wook Yun ◽  
Sung Hyun Kim
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Stability Criterion ◽  
Control Input ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Robust Stability Analysis ◽  
Time Systems ◽  
Varying Delay

This paper aims at deriving an efficient criterion for the robust stability analysis of discrete-time systems with time-varying delay. In the derivation, to obtain a larger stability region under the requirement of less computational complexity, this paper proposes a valuable method capable of establishing a less conservative stability criterion without using the free-weighting approach and an extremely augmented state. In parallel, the stabilization problem of systems with time-delayed control input is addressed in connection with the derived stability criterion.

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 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.

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