Delay-independent stability analysis of linear time-delay systems based on frequency discretization

This paper studies strong delay-independent stability of linear time-invariant systems. It is known that delay-independent stability of time-delay systems is equivalent to some frequency-dependent linear matrix inequalities. To reduce or eliminate conservatism of stability criteria, the frequency domain is discretized into several sub-intervals, and piecewise constant Lyapunov matrices are employed to analyze the frequency-dependent stability condition. Applying the generalized Kalman-Yakubovich-Popov lemma, new necessary and sufficient criteria are then obtained for strong delay-independent stability of systems with a single delay. The effectiveness of the proposed method is illustrated by a numerical example.

[1]  James Lam,et al.  Stabilization for state/input delay systems via static and integral output feedback , 2010, Autom..

[2]  E. W. Kamen,et al.  Linear systems with commensurate time delays: stability and stabilization independent of delay , 1982 .

[3]  Tetsuya Iwasaki,et al.  Parameter-dependent Lyapunov function for exact stability analysis of single-parameter dependent LTI systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  Huijun Gao,et al.  A New Model Transformation of Discrete-Time Systems With Time-Varying Delay and Its Application to Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[5]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[6]  Pierre-Alexandre Bliman,et al.  Lyapunov equation for the stability of linear delay systems of retarded and neutral type , 2002, IEEE Trans. Autom. Control..

[7]  Reinaldo M. Palhares,et al.  Delay-dependent robust H control of uncertain linear systems with lumped delays , 2005 .

[8]  Jin-Hua She,et al.  New delay-dependent stability criteria and stabilizing method for neutral systems , 2004, IEEE Trans. Autom. Control..

[9]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[10]  S. Niculescu.  H∞ memoryless control with an α-stability constraint for time-delay systems: an LMI approach , 1998, IEEE Trans. Autom. Control..

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

[12]  Jie Chen,et al.  Frequency sweeping tests for stability independent of delay , 1995, IEEE Trans. Autom. Control..

[13]  Maurício C. de Oliveira,et al.  Stability independent of delay using rational functions , 2009, Autom..

[14]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[15]  Heinz Unbehauen,et al.  Robust reliable control for a class of uncertain nonlinear state-delayed systems , 1999, Autom..

[16]  Huijun Gao,et al.  A Heuristic Approach to Static Output-Feedback Controller Synthesis With Restricted Frequency-Domain Specifications , 2014, IEEE Transactions on Automatic Control.

[17]  Graziano Chesi,et al.  Exact robust stability analysis of uncertain systems with a scalar parameter via LMIs , 2013, Autom..

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

[19]  C. Abdallah,et al.  Stability and Stabilization of Systems with Time Delay. Limitations and Opportunities , 2010 .

[20]  Huijun Gao,et al.  ${H}_{\infty }$ Filtering for Discrete-Time State-Delayed Systems With Finite Frequency Specifications , 2011, IEEE Transactions on Automatic Control.

[21]  Brian D. O. Anderson,et al.  Network Analysis and Synthesis: A Modern Systems Theory Approach , 2006 .

[22]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[23]  Jie Chen,et al.  On sufficient conditions for stability independent of delay , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[24]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[25]  L. Dugard,et al.  Dynamical compensation for time-delay systems An LMI approach , 2000 .

[26]  Karolos M. Grigoriadis,et al.  LPV Systems with parameter-varying time delays: analysis and control , 2001, Autom..

[27]  Ismail Ilker Delice,et al.  Delay-Independent Stability Test for Systems With Multiple Time-Delays , 2012, IEEE Transactions on Automatic Control.

[28]  Shinji Hara,et al.  Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma , 2007 .

[29]  Shinji Hara,et al.  Generalized KYP lemma: unified frequency domain inequalities with design applications , 2005, IEEE Transactions on Automatic Control.

[30]  Tomomichi Hagiwara,et al.  Exact Stability Analysis of 2-D Systems Using LMIs , 2006, IEEE Transactions on Automatic Control.

[31]  Jie Chen,et al.  On sufficient conditions for stability independent of delay , 1994, American Control Conference.

[32]  Min Wu,et al.  Augmented Lyapunov functional and delay‐dependent stability criteria for neutral systems , 2005 .

[33]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[34]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[35]  Pierre-Alexandre Bliman,et al.  An existence result for polynomial solutions of parameter-dependent LMIs , 2004, Syst. Control. Lett..

[36]  S. Niculescu.  Stability and hyperbolicity of linear systems with delayed state: a matrix-pencil approach , 1998 .

[37]  V. Kolmanovskii,et al.  On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems , 1999 .

[38]  Jianbin Qiu,et al.  A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[39]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[40]  Antonis Papachristodoulou,et al.  Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition , 2009, IEEE Transactions on Automatic Control.

[41]  Leopoldo García Franquelo,et al.  Selective Harmonic Mitigation Technique for Cascaded H-Bridge Converters With Nonequal DC Link Voltages , 2013, IEEE Transactions on Industrial Electronics.

[42]  Maurício C. de Oliveira,et al.  Synthesis of non-rational controllers for linear delay systems , 2004, Autom..

[43]  E. Fridman.  Stability of linear descriptor systems with delay: a Lyapunov-based approach , 2002 .

[44]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[45]  P. Agathoklis,et al.  Stability and the matrix Lyapunov equation for delay differential systems , 1989 .

[46]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..