A new double integral inequality and application to stability test for time-delay systems

Abstract This paper is concerned with stability analysis for linear systems with time delays. Firstly, a new double integral inequality is proposed. Then, it is used to derive a new delay-dependent stability criterion in terms of linear matrix inequalities (LMIs). Two numerical examples are given to demonstrate the effectiveness and merits of the present result.

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

[2]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[3]  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..

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

[5]  Wei Xing Zheng,et al.  Delay-dependent robust stabilization for uncertain neutral systems with distributed delays , 2007, Autom..

[6]  Li-Yun Yang,et al.  Delay-dependent robust stabilization for uncertain neutral systems with distributed delays , 2014 .

[7]  ParkPooGyeon,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011 .

[8]  Jin-Hoon Kim,et al.  Further improvement of Jensen inequality and application to stability of time-delayed systems , 2016, Autom..

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

[10]  H. Trinh,et al.  Refined Jensen-based inequality approach to stability analysis of time-delay systems , 2015 .

[11]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[12]  Yong He,et al.  Stability analysis of systems with time-varying delay via relaxed integral inequalities , 2016, Syst. Control. Lett..

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

[14]  PooGyeon Park,et al.  Second-order reciprocally convex approach to stability of systems with interval time-varying delays , 2014, Appl. Math. Comput..

[15]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[16]  Q. Han,et al.  New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities , 2014 .

[17]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..