Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

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

[2]  Vu Ngoc Phat,et al.  New exponential estimate for robust stability of nonlinear neutral time-delay systems with convex polytopic uncertainties , 2011 .

[3]  Hieu Trinh,et al.  New results on state bounding for discrete-time systems with interval time-varying delay and bounded disturbance inputs , 2014 .

[4]  Hieu Trinh,et al.  New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems , 2015 .

[5]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[6]  Vu Ngoc Phat,et al.  Improved delay-dependent exponential stability of singular systems with mixed interval time-varying delays , 2015 .

[7]  Thongchai Botmart,et al.  Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays , 2011, Appl. Math. Comput..

[8]  Vladimir L. Kharitonov,et al.  Exponential estimates for retarded time-delay systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

[9]  Vu Ngoc Phat,et al.  Exponential stability and stabilization of a class of uncertain linear time-delay systems , 2009, J. Frankl. Inst..

[10]  Pin-Lin Liu,et al.  Exponential stability for linear time-delay systems with delay dependence , 2003, J. Frankl. Inst..

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

[12]  Hieu Minh Trinh,et al.  A new approach to state bounding for linear time-varying systems with delay and bounded disturbances , 2014, Autom..

[13]  Phan Thanh Nam.  An improved criterion for exponential stability of linear systems with multiple time delays , 2008, Appl. Math. Comput..

[14]  Hamid Reza Feyzmahdavian,et al.  Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays , 2013, IEEE Transactions on Automatic Control.

[15]  Vu Ngoc Phat,et al.  LMI approach to exponential stability of linear systems with interval time-varying delays , 2012 .

[16]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[17]  Ju H. Park,et al.  Exponential stability of uncertain dynamic systems including state delay , 2006, Appl. Math. Lett..

[18]  S. M. Lee,et al.  Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach , 2008 .

[19]  Hong Gu,et al.  Asymptotic and exponential stability of uncertain system with interval delay , 2012, Appl. Math. Comput..

[20]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[21]  Ju H. Park,et al.  A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays , 2011, Appl. Math. Comput..

[22]  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..

[23]  Ju H. Park,et al.  New and improved results on stability of static neural networks with interval time-varying delays , 2014, Appl. Math. Comput..

[24]  Jiuwen Cao,et al.  Improved delay-dependent exponential stability criteria for time-delay system , 2013, J. Frankl. Inst..

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

[26]  Shengyuan Xu,et al.  Estimating stable delay intervals with a discretized Lyapunov-Krasovskii functional formulation , 2014, Autom..

[27]  Keqin Gu,et al.  Stability and Stabilization of Systems with Time Delay , 2011, IEEE Control Systems.

[28]  Ju H. Park,et al.  A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays , 2011, Appl. Math. Comput..

[29]  Shengyuan Xu,et al.  New Exponential Estimates for Time-Delay Systems , 2006, IEEE Transactions on Automatic Control.

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

[31]  Ju H. Park,et al.  Delay-dependent exponential stability criteria for neutral systems with interval time-varying delays and nonlinear perturbations , 2013, J. Frankl. Inst..

[32]  Hieu Minh Trinh,et al.  An enhanced stability criterion for time-delay systems via a new bounding technique , 2015, J. Frankl. Inst..

[33]  Pham Huu Anh Ngoc.  Stability of Positive Differential Systems With Delay , 2013, IEEE Transactions on Automatic Control.

[34]  Alexandr A. Zevin,et al.  Sharp Bounds for Lyapunov Exponents and Stability Conditions for Uncertain Systems With Delays , 2010, IEEE Transactions on Automatic Control.

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

[36]  Jinde Cao,et al.  Novel alpha-stability criterion of linear systems with multiple time delays , 2006, Appl. Math. Comput..

[37]  W. Steeb,et al.  Matrix Calculus and Kronecker Product: A Practical Approach to Linear and Multilinear Algebra , 2011 .