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

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.

• Publication year

  2020

• Venue

  Transactions of the Institute of Measurement and Control

• Publication date

  2020-09-10

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1177/0142331220947566
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• An Improved Local Stability Criterion for Digital Filters With Interference and Overflow Nonlinearity

  2020cited by this paper
• A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

  2018cited by this paper
• Stability of discrete-time systems with time-varying delay based on switching technique

  2018cited by this paper
• Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities

  2018cited by this paper
• DELAY-DEPENDENT STABILITY OF DISCRETE-TIME SYSTEMS WITH MULTIPLE DELAYS AND NONLINEARITIES

  2017cited by this paper
• Novel Summation Inequalities and Their Applications to Stability Analysis for Systems With Time-Varying Delay

  2017influential reference
• A delay-range-partition approach to analyse stability of linear systems with time-varying delays

  2016cited by this paper
• Summation inequality and its application to stability analysis for time-delay systems

  2016cited by this paper
• Delay-dependent Stability Analysis of Microgrid with Constant and Time-varying Communication Delays

  2016influential reference
• Improved stability results for uncertain discrete-time state-delayed systems in the presence of nonlinearities

  2016influential reference
• Passivity and Finite-Gain Performance for Two-Dimensional Digital Filters: The FM LSS Model Case

  2015cited by this paper
• Discrete Wirtinger-based inequality and its application

  2015influential reference
• Expected Power Bound for Two-Dimensional Digital Filters in the Fornasini-Marchesini Local State-Space Model

  2015cited by this paper
• Optimal partitioning method for stability analysis of continuous/discrete delay systems

  2015influential reference
• Stability of Discrete-Time Systems With Time-Varying Delays via a Novel Summation Inequality

  2015influential reference
• A New Delay-Dependent Stability Criterion for Uncertain 2-D Discrete Systems Described by Roesser Model Under the Influence of Quantization/Overflow Nonlinearities

  2015influential reference
• A new result on the delay‐dependent stability of discrete systems with time‐varying delays

  2014cited by this paper
• Lmi Control Toolbox For Use With Matlab

  2014cited by this paper
• Delay decomposition approach to robust delay-dependent H ∞ filtering of uncertain stochastic systems with time-varying delays

  2014cited by this paper
• Design of multiple controllers for networked control systems with delays and packet losses

  2013cited by this paper
• Delay-Partitioning Approach to H∞ Performance Analysis of Discrete-Time Systems with Interval Time-Varying Delay

  2013influential reference
• Stabilization of Interconnected Discrete Systems with Quantization and Overflow Nonlinearities

  2013cited by this paper
• Improved Delay-Dependent Stability Criteria for Discrete-Time Systems with Time-Varying Delays

  2013cited by this paper
• Note on stability of discrete-time time-varying delay systems

  2012influential reference
• Delay‐dependent LMI condition for global asymptotic stability of discrete‐time uncertain state‐delayed systems using quantization/overflow nonlinearities

  2011influential reference
• Reciprocally convex approach to stability of systems with time-varying delays

  2011cited by this paper
• New Stability Criteria for Linear Discrete-Time Systems With Interval-Like Time-Varying Delays

  2011cited by this paper
• Output Feedback Control of Discrete-Time Systems in Networked Environments

  2011cited by this paper
• Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay [Brief Paper]

  2010cited by this paper
• Technical communique: A delay-partitioning approach to the stability analysis of discrete-time systems

  2010influential reference
• LMI approach to stability of a class of discrete-time systems using two's complement arithmetic

  2010cited by this paper
• Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach

  2009cited by this paper
• An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities

  2009cited by this paper
• Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

  2009cited by this paper
• Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities

  2008cited by this paper
• Technical communique: Improved stability criterion and its applications in delayed controller design for discrete-time systems

  2008cited by this paper
• An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic

  2007cited by this paper
• New Results on Stability of Discrete-Time Systems With Time-Varying State Delay

  2007influential reference
• Stability of delay impulsive systems with application to networked control systems

  2007cited by this paper
• Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays

  2004cited by this paper
• YALMIP : a toolbox for modeling and optimization in MATLAB

  2004influential reference
• Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties

  2004cited by this paper
• Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks

  2002cited by this paper
• Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

  2001cited by this paper
• Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities

  2001cited by this paper
• Linear Matrix Inequalities in System and Control Theory

  1994influential reference
• Asymptotic stability of two-dimensional digital filters under quantization

  1994cited by this paper
• Finite wordlength effects in digital filters : a review

  1988cited by this paper
• Effects of quantization in second-order fixed-point digital filters with two's complement truncation quantizers

  1988cited by this paper
• Stability analysis of fixed- point digital filters using computer generated Lyapunov functions- Part I: Direct form and coupled form filters

  1985cited by this paper
• Suppression of limit cycles in digital filters designed with one magnitude-truncation quantizer

  1981cited by this paper

• Robust stability analysis of uncertain discrete-time delayed systems with finite wordlength nonlinearities via delay partitioning approach

  2024influential citation
• Stability of discrete-time system employing quantization and overflow nonlinearities

  2024cites this paper
• Stability of 2-D Discrete Systems in the Presence of Saturation Function and Delays

  2023cites this paper
• Delay partitioning approach to the delay-dependent stability of discrete-time systems with anti-windup

  2023cites this paper
• An anti-windup control strategy for discrete time-delay system based on triple Lyapunov functional

  2023cites this paper
• Stability of Interfered Digital Filters Subjected to Markovian Jumping Parameters and Time Delay Employing Quantization/Overflow Nonlinearities

  2021cites this paper
• Stability of Interfered Digital Filters Subjected to Markovian Jumping Parameters and Time Delay Employing Quantization/Overflow Nonlinearities

  2021cites this paper