An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay

Abstract The reciprocally convex combination lemma (RCCL) is an important technique to develop stability criteria for the systems with a time-varying delay. This note develops an extended reciprocally convex matrix inequality, which reduces the estimation gap of the RCCL-based matrix inequality and reduces the number of decision variables of the recently proposed delay-dependent RCCL. A stability criterion of a linear time-delay system is established through the proposed matrix inequality. Finally, a numerical example is given to demonstrate the advantage of the proposed method.

[1]  Hieu Minh Trinh,et al.  New finite-sum inequalities with applications to stability of discrete time-delay systems , 2016, Autom..

[2]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

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

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

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

[6]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Kun Liu,et al.  New conditions for delay-derivative-dependent stability , 2009, Autom..

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

[9]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[10]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

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

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

[13]  Yong He,et al.  An improved summation inequality to discrete-time systems with time-varying delay , 2016, Autom..

[14]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[15]  Emilia Fridman,et al.  Stability of systems with fast-varying delay using improved Wirtinger's inequality , 2013, 52nd IEEE Conference on Decision and Control.

[16]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

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

[19]  Yong He,et al.  Delay-Variation-Dependent Stability of Delayed Discrete-Time Systems , 2016, IEEE Transactions on Automatic Control.

[20]  HeYong,et al.  An improved summation inequality to discrete-time systems with time-varying delay , 2016 .

[21]  Jin-Hoon Kim,et al.  Note on stability of linear systems with time-varying delay , 2011, Autom..

[22]  Corentin Briat,et al.  Convergence and Equivalence Results for the Jensen's Inequality—Application to Time-Delay and Sampled-Data Systems , 2011, IEEE Transactions on Automatic Control.

[23]  Corentin Briat.  Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & Control , 2014 .

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

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

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

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

[28]  F. Gouaisbaut,et al.  Delay-dependent reciprocally convex combination lemma , 2016 .

[29]  Emilia Fridman,et al.  Stability of Discrete-Time Systems With Time-Varying Delays via a Novel Summation Inequality , 2015, IEEE Transactions on Automatic Control.