Iterative solution to linear matrix inequality arising from time delay descriptor systems

Applied Mathematics and Computation

Volumn 219, Issue 9, 2013, Pages 4176-4184

  Wang, Qing ^a   Xu, Pengcheng ^b   Lam, Edmund Y ^a   Wong, Ngai ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Descriptor system; Linear matrix equation (LME); Linear matrix inequality (LMI); Steepest descent method (SDM); Time delay system (TDS)

Indexed keywords

DESCRIPTOR SYSTEMS; FINITE MEMORY; HESSIAN MATRICES; INTERIOR-POINT METHOD; ITERATIVE ALGORITHM; ITERATIVE SOLUTIONS; LINEAR MATRIX EQUATIONS; LINEAR MATRIX INEQUALITY (LMIS); MATRIX FUNCTIONS; NEWTON'S METHODS; NUMERICAL EXAMPLE; OBJECTIVE FUNCTIONS; STORAGE REQUIREMENTS; STRICTLY CONVEXES; TIME-DELAY SYSTEMS;

ALGORITHMS; DESCRIBING FUNCTIONS; NEWTON-RAPHSON METHOD; STEEPEST DESCENT METHOD; TIME DELAY;

LINEAR MATRIX INEQUALITIES;

EID: 84871209067     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.11.017     Document Type: Article

References (28)

1. B. Du, J. Lam, Z. Shu, and Z. Wang A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components IET Control Theory & Applications 3 4 2009 383 390
2. S. Xu, and J. Lam A survey of linear matrix inequality techniques in stability analysis of delay systems International Journal of Systems Science 39 12 2008 1095 1113
3. S. Xu, and J. Lam On equivalence and efficiency of certain stability criteria for time-delay systems IEEE Transactions on Automatic Control 52 1 2007 95 101
4. Z.-G. Wu, J.H. Park, H. Su, and J. Chu Dissipativity analysis for singular systems with time-varying delays Applied Mathematics and Computation 218 8 2011 4605 4613
5. Z.-G. Wu, J.H. Park, H. Su, and J. Chu Admissibility and dissipativity analysis for discrete-time singular systems with mixed time-varying delays Applied Mathematics and Computation 218 13 2012 7128 7138
6. X. Wang, Q. Wang, Z. Zhang, Q. Chen, N. Wong, Balanced truncation for time-delay systems via approximate gramians, in: Design Automation Conference (ASP-DAC), 2011 16th Asia and South Pacific, 2011, pp. 55-60.
7. J. Lam, H. Gao, and C. Wang Stability analysis for continuous systems with two additive time-varying delay components Systems & Control Letters 56 1 2007 16 24
8. H. Gao, T. Chen, and J. Lam A new delay system approach to network-based control Automatica 44 1 2008 39 52
9. S. Xu, and J. Lam Robust Control and Filtering of Singular Systems Lecture Notes in Control and Information Sciences vol. 332 2006 Springer-Verlag Berlin
10. O. Kwon, and J.H. Park Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays Applied Mathematics and Computation 208 2009 58 68
11. C. Hua, X. Guan, and P. Shi Robust stabilization of a class of nonlinear time-delay systems Applied Mathematics and Computation 155 2004 737 752
12. H control for systems with time-varying delays Automatica 42 2 2006 343 348
13. S. Xu, J. Lam, and Y. Zou An improved characterization of bounded realness for singular delay systems and its applications International Journal of Robust and Nonlinear Control 18 3 2008 263 277
14. H control for networked systems with random communication delays IEEE Transactions on Automatic Control 51 3 2006 511 518
15. S. Boyd, L.E. Ghaoui, E. Feron, and N. Balakrishnan Linear Matrix Inequalities in System and Control Theory 1994 Society for Industrial and Applied Mathematics Philadelphia
16. P. Gunupudi, M. Nakhla, Multi-dimensional model reduction of VLSI interconnects, in: Proceedings of the Custom Integrated Circuits Conference (CICC), 2000, pp. 499-502.
17. P.K. Gunupudi, R. Khazaka, M.S. Nakhla, T. Smy, and D. Celo Passive parameterized time-domain macromodels for high-speed transmission-line networks IEEE Transactions on Microwave Theory and Techniques 51 12 2003 2347 2354
18. P. Gunupudi, R. Khazaka, and M. Nakhla Analysis of transmission line circuits using multidimensional model reduction techniques IEEE Transactions on Advanced Packaging 25 2 2002 174 180
19. S. Grivet-Talocia, S. Acquadro, C. Peraldo, F. Canavero, I. Icelander, M. Rouvala, A. Arslan, Parameterized macromodels for lossy multiconductor transmission lines, in: Proceedings of the International Zurich Symposium on Electromagnetic Compatibility (EMC-Zurich), 2006, pp. 93-96.
20. B. Zhou, J. Lam, and G.-R. Duan Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations Computers & Mathematics with Applications 56 12 2008 3070 3078
21. Z.-Y. Li, B. Zhou, J. Lam, and Y. Wang Positive operator based iterative algorithms for solving Lyapunov equations for itô stochastic systems with markovian jumps Applied Mathematics and Computation 217 2011 8179 8195
22. P. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein Distributed optimization and statistical learning via the alternating direction method of multipliers Foundations and Trends in Machine Learning 3 2010 1 122
23. R.A. Horn, and C.R. Johnson Matrix Analysis 1985 Cambridge University Press Cambridge
24. M. Chen, and X. Li An estimation of the spectral radius of a product of block matrices Linear Algebra & Its Applications 379 2004 267 275
25. Q. Wang, J. Lam, Y. Wei, and T. Chen Iterative solutions of coupled discrete Markovian jump Lyapunov equations Computers & Mathematics with Applications 55 4 2008 843 850
26. Y. Chahlaoui, P. Van Dooren, A collection of benchmark examples for model reduction of linear time invariant dynamical systems, Available from: , SLICOT Working Note, 2002.
27. K. Verheyden, K. Green, and D. Roose Numerical stability analysis of a large-scale delay system modeling a lateral semiconductor laser subject to optical feedback Physical Review E 69 2004 036702
28. W. Michiels, and S.-I. Niculescu Stability and Stabilization of Time-Delay Systems 2007 Society for Industrial and Applied Mathematics Philadelphia PA, USA