Improved stability criteria for linear systems with interval time-varying delays: Generalized zero equalities approach

This paper suggests first-order and second-order generalized zero equalities and constructs a new flexible Lyapunov-Krasovskii functional with more state terms. Also, by applying various zero equalities, improved stability criteria of linear systems with interval time-varying delays are developed. Using Wirtinger-based integral inequality, Jensen inequality and a lower bound lemma, the time derivative of the Lyapunov-Krasovskii functional is bounded by the combinations of various state terms including not only integral terms but also their interval-normalized versions, which contributes to make the stability criteria less conservative. Numerical examples show the improved performance of the criteria in terms of maximum delay bounds.

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

[2]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[3]  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..

[4]  Ju H. Park,et al.  Improved approaches to stability criteria for neural networks with time-varying delays , 2013, J. Frankl. Inst..

[5]  Bin Yang,et al.  New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique , 2015 .

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

[7]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[8]  Shengyuan Xu,et al.  Fuzzy H ∞ filtering for nonlinear Markovian jump neutral systems , 2011, Int. J. Syst. Sci..

[9]  Keqin Gu.  Discretized Lyapunov functional for uncertain systems with multiple time-delay , 1999 .

[10]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[11]  Peng Shi,et al.  A novel approach on stabilization for linear systems with time-varying input delay , 2012, Appl. Math. Comput..

[12]  Changyun Wen,et al.  Improved delay-range-dependent stability criteria for linear systems with interval time-varying delays [Brief Paper] , 2012 .

[13]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

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

[15]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[16]  Sung Hyun Kim,et al.  Improved approach to robust stability and H∞ performance analysis for systems with an interval time-varying delay , 2012, Appl. Math. Comput..

[17]  Wei Xing Zheng,et al.  Stability Analysis of Time-Delay Neural Networks Subject to Stochastic Perturbations , 2013, IEEE Transactions on Cybernetics.

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

[19]  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..

[20]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

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

[22]  Xun-lin Zhu,et al.  Brief paper New stability criteria for continuous-time systems with interval time-varying delay , 2010 .

[23]  Shengyuan Xu,et al.  Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays , 2012, J. Frankl. Inst..

[24]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[25]  PooGyeon Park,et al.  Robust Η/ spl alpha/ stabilisation of networked control systems with packet analyser [Brief Paper] , 2010 .

[26]  Ju H. Park,et al.  Analysis on robust H∞ performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov-Krasovskii functional , 2013, Appl. Math. Comput..

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

[28]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .