Balanced truncation approach to model reduction of Markovian jump time-varying delay systems

Journal of the Franklin Institute

Volumn 352, Issue 10, 2015, Pages 4205-4224

  Zhang, Huiyan ^a   Wu, Ligang ^a   Shi, Peng ^b,c   Zhao, Yuxin ^d  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF ADELAIDE   (Australia)

^c VICTORIA UNIVERSITY   (Australia)

^d HARBIN ENGINEERING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; LINEAR SYSTEMS; LINEAR TRANSFORMATIONS; MARKOV PROCESSES; MATRIX ALGEBRA; STOCHASTIC SYSTEMS; TIME DELAY; TIME VARYING CONTROL SYSTEMS;

DISSIPATION INEQUALITY; MARKOVIAN JUMP LINEAR SYSTEMS; MODEL REDUCTION PROBLEMS; REDUCED ORDER MODELS; STOCHASTIC STABILITY; TIME VARYING DELAY SYSTEMS; TIME VARYING- DELAYS; TRANSFORMATION MATRICES;

CONTINUOUS TIME SYSTEMS;

EID: 84940591381     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2015.05.041     Document Type: Article

References (35)

1. P. Shi, Y. Yin, F. Liu, and J. Zhang Robust control on saturated Markov jump systems with missing information Inf. Sci. 265 2014 123 138
2. infin; control for network control systems with Markovian jumps and time delays Int. J. Innov. Comput., Inf. Control 9 2013 4889 4902
3. H. Chen, C. Zhu, P. Hu, and Y. Zhang Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays Nonlinear Dyn. 69 2012 1023 1039
4. H. Huang, F. Long, and C. Li Stabilization for a class of Markovian jump linear systems with linear fractional uncertainties Int. J. Innov. Comput., Inf. Control 11 2015 295 307
5. infin; control and filtering for uncertain Markovian jump systems with time-varying delays IEEE Trans. Circuits Syst.-I: Regul. Pap. 54 2007 2070 2077
6. infin; model reduction of Markovian jump linear systems Syst. Control Lett. 50 2003 103 118
7. G. Kotsalis, A. Megretski, and M.A. Dahleh Balanced truncation for a class of stochastic jump linear systems and model reduction for hidden Markov models IEEE Trans. Autom. Control 53 2008 2543 2557
8. G. Kotsalis, A. Megretski, and M.A. Dahleh Balanced truncation for discrete time Markov jump linear systems IEEE Trans. Autom. Control 55 2010 2606 2611
9. infin; model reduction for linear time-delay systems: continuous-time case Int. J. Control 74 2001 1062 1074
10. infin; model reduction for discrete time-delay systems: delay-independent and dependent approaches Int. J. Control 77 2004 321 335
11. M. Wu, Y. He, J. She, and et al. Delay-dependent criteria for robust stability of time-varying delay systems Automatica 40 2004 1435 1439
12. P.G. Park, J.W. Ko, and C. Jeong Reciprocally convex approach to stability of systems with time-varying delays Automatica 47 2011 235 238
13. G. Lastman Reduced-order aggregated models for bilinear time-invariant dynamical systems IEEE Trans. Autom. Control 29 1984 359 361
14. L ∞-error bounds Int. J. Control 39 1984 1115 1193
15. H. Gao, J. Lam, C. Wang, and Q. Wang Hankel norm approximation of linear systems with time-varying delay: continuous and discrete cases Int. J. Control 77 2004 1503 1520
16. infin; model reduction for linear switched systems with time-varying delay Automatica 45 2009 186 193
17. B. Moore Principal component analysis in linear systems: controllability, observability, and model reduction IEEE Trans. Autom. Control 26 1981 17 32
18. A.C. Antoulas, D.C. Sorensen, and S. Gugercin A survey of model reduction methods for large-scale systems Contemp. Math. 280 2001 193 220
19. S. Gugercin, and A.C. Antoulas A survey of model reduction by balanced truncation and some new results Int. J. Control 77 2004 748 766
20. M. Green A relative error bound for balanced stochastic truncation IEEE Trans. Autom. Control 33 1988 961 965
21. H. Sandberg, and A. Rantzer Balanced truncation of linear time-varying systems IEEE Trans. Autom. Control 49 2004 217 229
22. L. Zhang, B. Huang, and T. Chen Model reduction of uncertain systems with multiplicative noise based on balancing SIAM J. Control Optim. 45 2006 1541 1560
23. N. Monshizadeh, H. Trentelman, and M. Camlibel A simultaneous balanced truncation approach to model reduction of switched linear systems IEEE Trans. Autom. Control 57 2012 3118 3131
24. H.R. Shaker, and R. Wisniewski Generalised gramian framework for model/controller order reduction of switched systems Int. J. Syst. Sci. 42 2011 1277 1291
25. H.R. Shaker, and R. Wisniewski Model reduction of switched systems based on switching generalized gramians Int. J. Innov. Comput., Inf. Control 8 2012 5025 5044
26. M. Petreczky, R. Wisniewski, and J. Leth Balanced truncation for linear switched systems Nonlinear Anal.: Hybrid Syst. 10 2013 4 20
27. X. Wang, Q. Wang, Z. Zhang, et al. Balanced truncation for time-delay systems via approximate gramians, in: Design Automation Conference (ASP-DAC), 2011, pp. 55-60.
28. E. Jarlebring, T. Damm, and W. Michiels Model reduction of time-delay systems using position balancing and delay Lyapunov equations Math. Control, Signals, Syst. 25 2013 147 166
29. J.C. Willems Dissipative dynamical systems. Part I. General theory Arch. Ration. Mech. Anal. 45 1972 321 351
30. J.C. Willems Dissipative dynamical systems. Part II. Linear systems with quadratic supply rates Arch. Ration. Mech. Anal. 45 1972 352 393
31. S. Xie, L. Xie, and C.E. de Souza Robust dissipative control for linear systems with dissipative uncertainty Int. J. Control 70 1998 169 191
32. H. Shao Improved delay-dependent stability criteria for systems with a delay varying in a range Automatica 44 2008 2008 3215 3218
33. C. Kenney, and G. Hewer Necessary and sufficient conditions for balancing unstable systems IEEE Trans. Autom. Control 32 2008 1987 157 160
34. K. Zhou, G. Salomon, and E. Wu Balanced realization and model reduction for unstable systems Int. J. Robust Nonlinear Control 9 1999 183 198
35. M. Farhood, and G.E. Dullerud Model reduction of nonstationary LPV systems IEEE Trans. Autom. Control 52 2007 181 196