HSH-norm optimal MOR for the MIMO linear time-invariant systems on the Stiefel manifold

References

• Absil, P. A., Mahony, R., & Sepulchre, R. 2008). Optimization algorithms on matrix manifolds. Princeton University Press.
   Google Scholar
• Antoulas, A. C. (2005). Approximation of large-scale dynamical systems. SIAM.
   Google Scholar
• Benner, P., Cao, X., & Schilders, W. (2019). A bilinear H2 model order reduction approach to linear parameter-varying systems. Advances in Computational Mathematics, 45(5–6), 2241–2271. https://doi.org/10.1007/s10444-019-09695-9
   Web of Science ®Google Scholar
• Benner, P., Grivet-Talocia, S., Quarteroni, A., Rozza, G., Schilders, W., & Silveira, L. M. (2021). Model order reduction, volume 3: Applications. Walter de Gruyter GmbH & Co KG.
   Google Scholar
• Bunse-Gerstner, A., Kubalińska, D., Vossen, G., & Wilczek, D. (2010). H2-norm optimal model reduction for large scale discrete dynamical MIMO systems. Journal of Computational and Applied Mathematics, 233(5), 1202–1216. https://doi.org/10.1016/j.cam.2008.12.029
   Web of Science ®Google Scholar
• Chahlaoui, Y., & Dooren, P. V. (2005). Benchmark examples for model reduction of linear time-invariant dynamical systems. In Lecture notes in computational science and engineering (pp. 379–392). Springer, Berlin Heidelberg.
   Google Scholar
• Fernando, K., & Nicholson, H. (1982). Minimality of SISO linear systems. Proceedings of the IEEE, 70(10), 1241–1242. https://doi.org/10.1109/PROC.1982.12460
   Web of Science ®Google Scholar
• Freund, R. W. (2000). Krylov-subspace methods for reduced-order modeling in circuit simulation. Journal of Computational and Applied Mathematics, 123(1-2), 395–421. https://doi.org/10.1016/S0377-0427(00)00396-4
   Web of Science ®Google Scholar
• Gallivan, K., Grimme, G., & Dooren, P. V. (1996). A rational Lanczos algorithm for model reduction. Numerical Algorithms, 12(1), 33–63. https://doi.org/10.1007/BF02141740
   Web of Science ®Google Scholar
• Glover, K. (1984). All optimal Hankel-norm approximations of linear multivariable systems and L∞-error bounds. International Journal of Control, 39(6), 1115–1193. https://doi.org/10.1080/00207178408933239
   Web of Science ®Google Scholar
• Gugercin, S., Antoulas, A. C., & Beattie, C. (2008). H2 model reduction for large-scale linear dynamical systems. SIAM Journal on Matrix Analysis and Applications, 30(2), 609–638. https://doi.org/10.1137/060666123
   Web of Science ®Google Scholar
• Hanzon, B. (1992). The area enclosed by the (oriented) Nyquist diagram and the Hilbert–Schmidt-Hankel-norm of a linear system. IEEE Transactions on Automatic Control, 37(6), 835–839. https://doi.org/10.1109/9.256345
   Web of Science ®Google Scholar
• Jiang, Y. L., & Chen, H. B. (2012). Time domain model order reduction of general orthogonal polynomials for linear input–output systems. IEEE Transactions on Automatic Control, 57(2), 330–343. https://doi.org/10.1109/TAC.2011.2161839
   Web of Science ®Google Scholar
• Jiang, Y. L., & Xu, K. L. (2017). H2 optimal reduced models of general MIMO LTI systems via the cross Gramian on the Stiefel manifold. Journal of the Franklin Institute, 354(8), 3210–3224. https://doi.org/10.1016/j.jfranklin.2017.02.019
   Web of Science ®Google Scholar
• Lee, K. H., & Huang, B. (2009). H∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation. International Journal of Systems Science, 40(7), 685–693. https://doi.org/10.1080/00207720902953102
   Web of Science ®Google Scholar
• Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26(1), 17–32. https://doi.org/10.1109/TAC.1981.1102568
   Web of Science ®Google Scholar
• Salimbahrami, B., & Lohmann, B. (2006). Order reduction of large scale second-order systems using Krylov subspace methods. Linear Algebra and Its Applications, 415(2), 385–405. https://doi.org/10.1016/j.laa.2004.12.013
   Web of Science ®Google Scholar
• Sato, H. (2015, October). A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions. Computational Optimization and Applications, 64(1), 101–118. https://doi.org/10.1007/s10589-015-9801-1
   Web of Science ®Google Scholar
• Sato, H., & Sato, K. (2015, December). Riemannian trust-region methods for H2 optimal model reduction. 2015 54th IEEE Conference on Decision and Control (CDC) (pp. 4648–4655). IEEE.
   Google Scholar
• Sato, H., & Sato, K. (2016). A new H2 optimal model reduction method based on Riemannian conjugate gradient method. 2016 IEEE 55th Conference on Decision and Control (CDC) (pp. 5762–5768). IEEE.
   Google Scholar
• Schelfhout, G. (1996). Model reduction for control design (Unpublished doctoral dissertation). Dept. Electrical Engineering, KU Leuven, Belgium.
   Google Scholar
• Tombs, M. S., & Postlethwaite, I. (1987). Truncated balanced realization of a stable non-minimal state-space system. International Journal of Control, 46(4), 1319–1330. https://doi.org/10.1080/00207178708933971
   Web of Science ®Google Scholar
• Tong, D. B., Zhou, W. N., Gao, Y., Ji, C., & Su, H. Y. (2013). H∞ model reduction for port-controlled Hamiltonian systems. Applied Mathematical Modelling, 37(5), 2727–2736. https://doi.org/10.1016/j.apm.2012.06.031
   Web of Science ®Google Scholar
• Wang, X. L., & Jiang, Y. L. (2016). Model reduction of discrete-time bilinear systems by a Laguerre expansion technique. Applied Mathematical Modelling, 40(13), 6650–6662. https://doi.org/10.1016/j.apm.2016.02.015
   Web of Science ®Google Scholar
• Wang, Z. D., & Unbehauen, H. (1999). Model reduction based on regional pole and covariance equivalent realizations. IEEE Transactions on Automatic Control, 44(10), 1889–1893. https://doi.org/10.1109/9.793730
   Web of Science ®Google Scholar
• Wolf, T., & Panzer, H. (2015). The ADI iteration for Lyapunov equations implicitly H2 pseudo-optimal model order reduction. International Journal of Control, 89(3), 481–493. https://doi.org/10.1080/00207179.2015.1081985
   Web of Science ®Google Scholar
• Xu, Y. S., & Lam, J. (2003). H∞ model reduction for discrete-time singular systems. Systems & Control Letters, 48(2), 121–133. https://doi.org/10.1016/S0167-6911(02)00279-7
   Web of Science ®Google Scholar
• Xu, Y. S., & Zeng, T. S. (2011). Optimal H2 model reduction for large scale MIMO system via tangential interpolation. International Journal of Numerical Analysis and Modeling, 8(1), 174–188. http://www.math.ualberta.ca/ijnam/Volume-8-2011/No-1-11/2011-01-10.pdf
   Web of Science ®Google Scholar
• Yan, W. Y., & Lam, J. (1999). An approximate approach to H2 optimal model reduction. IEEE Transactions on Automatic Control, 44(7), 1341–1358. https://doi.org/10.1109/9.774107
   Web of Science ®Google Scholar
• Zhang, H., Wu, L., Shi, P., & Zhao, Y. (2015). Model reduction on Markovian jump systems with partially unknown transition probabilities: Balanced truncation approach. IET Control Theory & Applications, 9(9), 1411–1421. https://doi.org/10.1049/cth2.v9.9
   Web of Science ®Google Scholar
• Zhu, X. J. (2016). A Riemannian conjugate gradient method for optimization on the Stiefel manifold. Computational Optimization and Applications, 67(1), 73–110. https://doi.org/10.1007/s10589-016-9883-4
   Web of Science ®Google Scholar