New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities

Summary Stability conditions for time-delay systems using the Lyapunov-based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time-varying delays. A double-integral inequality is derived inspired by Wirtinger-based single-integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses.

[1]  Derong Liu.  TNNLS Call for Reviewers and Special Issues , 2015, IEEE Trans. Neural Networks Learn. Syst..

[2]  Ju H. Park,et al.  Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay , 2013, Circuits, Systems, and Signal Processing.

[3]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[4]  A. Wu,et al.  Improved Stability Criteria for Linear Neutral Time‐Delay Systems , 2015 .

[5]  Yuzhi Liu,et al.  Improved robust stabilization method for linear systems with interval time-varying input delays by using Wirtinger inequality. , 2015, ISA transactions.

[6]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[7]  Frédéric Gouaisbaut,et al.  Hierarchy of LMI conditions for the stability analysis of time-delay systems , 2015, Syst. Control. Lett..

[8]  PooGyeon Park,et al.  Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functionals , 2015, Neurocomputing.

[9]  Xin Zhou,et al.  Delay-partitioning approach for systems with interval time-varying delay and nonlinear perturbations , 2015, J. Comput. Appl. Math..

[10]  Emilia Fridman,et al.  Tutorial on Lyapunov-based methods for time-delay systems , 2014, Eur. J. Control.

[11]  Q. Han,et al.  Novel delay‐derivative‐dependent stability criteria using new bounding techniques , 2013 .

[12]  Yuanqing Xia,et al.  New results on stability and stabilisation of systems with interval time-varying delay , 2011 .

[13]  Ju H. Park,et al.  Stability of time-delay systems via Wirtinger-based double integral inequality , 2015, Autom..

[14]  Guoping Liu,et al.  Improved delay-range-dependent stability criteria for linear systems with time-varying delays , 2010, Autom..

[15]  Jian Sun,et al.  Less conservative stability criteria for linear systems with interval time‐varying delays , 2015 .

[16]  Ju H. Park,et al.  Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality , 2014, J. Frankl. Inst..

[17]  Guanghong Yang,et al.  Optimal partitioning method for stability analysis of continuous/discrete delay systems , 2015 .

[18]  Chun-Yi Su,et al.  Neural-Adaptive Control of Single-Master–Multiple-Slaves Teleoperation for Coordinated Multiple Mobile Manipulators With Time-Varying Communication Delays and Input Uncertainties , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[19]  PooGyeon Park,et al.  Improved criteria on robust stability and H∞ performance for linear systems with interval time-varying delays via new triple integral functionals , 2014, Appl. Math. Comput..

[20]  Jun Cheng,et al.  Further improvement in delay-dependent stability criteria for continuous-time systems with time-varying delays , 2015, Neurocomputing.

[21]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..

[22]  Ju H. Park,et al.  On stability criteria for neural networks with time-varying delay using Wirtinger-based multiple integral inequality , 2015, J. Frankl. Inst..

[23]  Salah Laghrouche,et al.  Adaptive-Gain Second Order Sliding Mode Observer Design for Switching Power Converters , 2013, ArXiv.

[24]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[25]  C. Wang,et al.  Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay , 2012 .

[26]  Xin Zhou,et al.  On improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay , 2015, Int. J. Autom. Comput..