Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

2009 ◽  
Vol 143 (2) ◽  
pp. 329-355 ◽  
Author(s):  
M. S. Mahmoud ◽  
Y. Xia
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Stability And Stabilization ◽  
Time Systems ◽  
Robust Stability And Stabilization

scholarly journals New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays

2020 ◽  
pp. 014233122094756
Author(s):  
Kalpana Singh ◽  
V Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Discrete Time ◽  
Time Varying ◽  
Delay Bound ◽  
Discrete Time Systems ◽  
Forward Difference ◽  
Convex Inequality ◽  
Time Systems ◽  
Delay Partitioning

This paper is associated with the problem of robust stability of discrete-time systems with time-varying delays and finite wordlength nonlinearities. The main contribution of the paper is two-fold. First, this paper presents a new Lyapunov function based on the idea of partitioning the delay interval into subintervals. The approach may be considered as an advancement over the several existing approaches where only the lower delay bound is partitioned. The second is that reciprocally convex inequality (RCI) and Wirtinger-based inequality (WBI) are used to estimate the sum terms involved in the forward difference of Lyapunov function. The intermediate delay is also included in the Lyapunov function to deal with the delay information more effectively. Finally, several examples are provided to illustrate the less conservatism of the proposed approach as compared to several 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.

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