An improved delay-dependent stability criterion of networked control systems

This paper presents a new stability analysis of networked control systems (NCSs) with network-induced delay and packet dropout. A novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which takes into account the feature of the sawtooth delay induced by sample-and-hold. Based on an improved version of Wirtinger's inequality and the convex combination method, a delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The advantage of the proposed criterion lies in its simplicity and less conservativeness than some of the existing results. The new criterion is applied to the network-based state feedback control problems. Numerical examples are given to verify the effectiveness of the proposed criterion.

[1]  Frédéric Gouaisbaut,et al.  On the Use of the Wirtinger Inequalities for Time-Delay Systems , 2012, TDS.

[2]  Hamid Reza Karimi,et al.  A new design of H∞ filtering for continuous-time Markovian jump systems with time-varying delay and partially accessible mode information , 2013, Signal Process..

[3]  Zhi-Hong Guan,et al.  Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems , 2004, Autom..

[4]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[5]  L. Rodrigues,et al.  On exponential stability of linear networked control systems , 2014 .

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

[7]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[8]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[9]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[10]  M. Fei,et al.  A refined delay-partitioning approach to the stability of linear systems with interval time-varying delays , 2013, 2013 IEEE International Symposium on Industrial Electronics.

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

[12]  Dong Yue,et al.  Delay-fractioning-dependent robust H ∞ control for linear systems with delay in state or input and its applications , 2012, Int. J. Syst. Sci..

[13]  Guang-Hong Yang,et al.  Sampled-data H ∞ control for networked control systems with digital control inputs , 2012, Int. J. Syst. Sci..

[14]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

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

[16]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

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

[18]  E. Fridman,et al.  Networked‐based stabilization via discontinuous Lyapunov functionals , 2012 .

[19]  Alexandre Seuret,et al.  Jensen's and Wirtinger's Inequalities for Time-Delay Systems , 2013, TDS.

[20]  Min Wu,et al.  Improved stabilisation method for networked control systems , 2007 .

[21]  Guang-Hong Yang,et al.  New results on stability analysis of networked control systems , 2008, 2008 American Control Conference.

[22]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[23]  Jianbin Qiu,et al.  Improved Delay-Dependent $H_{\infty }$ Filtering Design for Discrete-Time Polytopic Linear Delay Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Qing-Long Han,et al.  Delay-dependent robust stability for uncertain linear systems with interval time-varying delay , 2006, Autom..

[25]  Wei Qian,et al.  New stability analysis for systems with interval time-varying delay , 2013, J. Frankl. Inst..

[26]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[27]  Frédéric Gouaisbaut,et al.  An augmented model for robust stability analysis of time-varying delay systems , 2009, Int. J. Control.

[28]  João Pedro Hespanha,et al.  Exponential stability of impulsive systems with application to uncertain sampled-data systems , 2008, Syst. Control. Lett..

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

[30]  Huijun Gao,et al.  Network-Based ${{\cal H}}_{\!\!\!\infty }$ Output Tracking Control , 2008, IEEE Transactions on Automatic Control.