An efficient hybrid reduction method for time-delay systems using Hermite expansions

References

• Antoulas, A. C . (2005). Approximation of large-scale dynamical system . Philadelphia, PA: SIAM.
   Google Scholar
• Bai, Z. J. , & Su, Y. F. (2005). Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method. SIAM Journal on Scientific Computing, 26 (5), 1692–1709.
   Web of Science ®Google Scholar
• Baur, U. , Benner, P. , & Feng, L. H. (2014). Model order reduction for linear and nonlinear systems: A system-theoretic perspective. Archives of Computational Methods in Engineering, 21 (4), 331–358.
   Web of Science ®Google Scholar
• Eid, R. , & Lohmann, B . (2008). Moment matching model order reduction in time domain via Laguerre series. In Proceedings of the 17th IFAC World congress (Vol. 41, pp. 3198–3203). Seoul.
   Google Scholar
• Ferranti, F. , Nakhla, M. , Antonini, G. , Dhaene, T. , Knockaert, L. , & Ruehli, A. E. (2012). Interpolation-based parameterized model order reduction of delayed systems. IEEE Transactions on Microwave Theory and Techniques, 60 (3), 431–440.
   Web of Science ®Google Scholar
• Gastelletti, A. , Galelli, S. , Ratto, M. , Soncini-Sessa, R. , & Young, P. C. (2012). A general framework for dynamic emulation modelling in environmental problems. Environmental Modelling & Software, 34 , 5–18.
   Web of Science ®Google Scholar
• Gugercin, S. , Antoulas, A. C. , & Beattie, C. (2008). Model reduction for large-scale linear dynamical systems. SIAM Journal on Matrix Analysis and Applications, 30 (2), 609–638.
   Web of Science ®Google Scholar
• Jarlebring, E. , Damm, T. , & Michiels, W. (2013). Model reduction of time-delay systems using position balancing and delay Lyapunov equations. Mathematics of Control, Signals, and Systems, 25 (2), 147–166.
   Web of Science ®Google Scholar
• Lam, J. (1993). Model reduction of delay systems using Páde approximants. International Journal of Control, 57 (2), 377–391.
   Web of Science ®Google Scholar
• Lam, J. , Gao, H. , & Wang, C. (2005). H ∞ model reduction of linear systems with distributed delay. IEE Proceedings – Control Theory and Applications, 152 (6), 662–674.
   Google Scholar
• Michiels, W. , Jarlebring, E. , & Meerbergen, K. (2011). Krylov-based model order reduction of time-delay systems. SIAM Journal on Matrix Analysis and Applications, 32 (4), 1399–1421.
   Web of Science ®Google Scholar
• Qiu, J. B. , Gao, H. J. , & Ding, S. X. (2016). Recent advances on fuzzy-model-based nonlinear networked control systems: A survey. IEEE Transactions on Industrial Electronics, 63 (2), 1207–1217.
   Web of Science ®Google Scholar
• Rasekh, E. , & Dounavis, A. (2012). Multiorder Arnoldi approach for model order reduction of PEEC models with retardation. IEEE Transactions on Components, Packaging and Manufacturing Technology, 2 (10), 1629–1636.
   Web of Science ®Google Scholar
• Saadvandi, M. , Meerbergen, K. , & Jarlebring, E. (2012). On dominant poles and model reduction of second order time-delay systems. Applied Numerical Mathematics, 62 (1), 21–34.
   Web of Science ®Google Scholar
• Samuel, E. R. , Knockaert, L. , & Dhaene, T. (2014). Model order reduction of time-delay systems using a Laguerre expansion technique. IEEE Transactions on Circuits and Systems I Regular Papers, 61 (6), 1815–1823.
   Web of Science ®Google Scholar
• Scarciotti, G. , & Astolfi, A . (2014). Model reduction by moment matching for linear time-delay systems. In Proceedings of the International Federation of Automatic Control (Vol. 47, pp. 9462–9467).
   Google Scholar
• Scarciotti, G. , & Astolfi, A. (2016). Model reduction of neutral linear and nonlinear time-invariant time-delay systems with discrete and distributed delays. IEEE Transactions on Automatic Control, 61 (6), 1438–1451.
   Web of Science ®Google Scholar
• Smith, H . (2011). An introduction to delay differential equations with applications to the life sciences . New York, NY: Springer-Verlag.
   Google Scholar
• Szegö, G . (1939). Orthogonal polynomials . New York, NY: American Mathematical Society.
   Google Scholar
• Tych, W. , & Young, P. C. (2012). A Matlab software framework for dynamic model emulation. Environmental Modelling & Software, 34 , 19–29.
   Web of Science ®Google Scholar
• Wang, Q. , Wang, Y. Z. , Lam, E. Y. , & Wong, N. (2013). Model order reduction for neutral systems by moment matching. Circuits, Systems and Signal Processing, 32 (3), 1039–1063.
   Web of Science ®Google Scholar
• Wang, T. , Gao, H. J. , & Qiu, J. B. (2016). A combined fault-tolerant and predictive control for network-based industrial processes. IEEE Transactions on Industrial Electronics, 63 (4), 2529–2536.
   Web of Science ®Google Scholar
• Wang, T. , Qiu, J. B. , & Gao, H. J. (2017). Adaptive neural control of stochastic nonlinear time-delay systems with multiple constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems, Advance online publication. doi:10.1109/TSMC.2016.2562511
   Web of Science ®Google Scholar
• Wang, T. , Qiu, J. B. , Yin, S. , Gao, H. J. , Fan, J. L. , & Chai, T. Y. (2016). Performance-based adaptive fuzzy tracking control for networked industrial processes. IEEE Transactions on Cybernetics, 46 (8), 1760–1770.
   PubMed Web of Science ®Google Scholar
• Wang, X. , Zhang, Z. , Wang, Q. , & Wong, N. (2014). Gramian-based model order reduction of parameterized time-delay systems. International Journal of Circuit Theory and Applications, 42 (7), 687–706.
   Web of Science ®Google Scholar
• Wang, X. L. , & Jiang, Y. L. (2011). Model order reduction methods for coupled systems in the time domain using Laguerre polynomials. Computers and Mathematics with Applications, 62 (8), 3241–3250.
   Web of Science ®Google Scholar
• Wang, X. L. , & Jiang, Y. L. (2014). On model reduction of K-power bilinear systems. International Journal of Systems Science, 45 (9), 1978–1990.
   Web of Science ®Google Scholar
• Wei, Y. H. , Hu, Y. S. , Dai, Y. , & Wang, Y. (2016). A generalized Páde approximation of time delay operator. International Journal of Control Automation and Systems, 14 (1), 181–187.
   Web of Science ®Google Scholar
• Wu, L. G. , & Zheng, W. X. (2009). Weighted H ∞ model reduction for linear switched systems with time-varying delay. Automatica, 45 (1), 186–193.
   Web of Science ®Google Scholar
• Xu, S. Y. , & Lam, J. (2008). A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science, 39 (12), 1095–1113.
   Web of Science ®Google Scholar
• Yang, R. , Gao, H. , Lam, J. , & Shi, P. (2009). New stability criteria for neural networks with distributed and probabilistic delays. Circuits, Systems and Signal Processing, 28 , 505–522.
   Web of Science ®Google Scholar
• Yin, X. Y. , Li, Z. J. , Zhang, L. X. , Wang, C. H. , Shammakh, W. , & Ahmad, B. (2015). Model reduction of a class of Markov jump nonlinear systems with time-varying delays via projection approach. Neurocomputing, 166 , 436–446.
   Web of Science ®Google Scholar
• Young, P. C . (2011). Recursive estimation and time-series analysis: An introduction for the student and practitioner . Berlin: Springer-Verlag.
   Google Scholar
• Young, P. C. , & Ratto, M. (2009). A unified approach to environmental systems modelling. Stochastic Environmental Research and Risk Assessment, 23 , 1037–1057.
   Web of Science ®Google Scholar
• Yin, X. Y. , Zhang, X. , Zhang, L. X. , Wang, C. H. , Al-Yami, M. , & Hayat, T. (2015). H ∞ model approximation for discrete-time Takagi–Sugeno fuzzy systems with Markovian jumping parameters. Neurocomputing, 157 , 306–314.
   Web of Science ®Google Scholar
• Zhang, Y. J. , & Su, Y. F. (2013). A memory-efficient model order reduction for time-delay systems. BIT Numerical Mathematics, 53 (4), 1047–1073.
   Web of Science ®Google Scholar