Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions

References

• Antoulas, A. C. (2005). Approximation of large-scale dynamical systems. SIAM.
   Google Scholar
• Antsaklis, P. J., & Michel, A. N. (2006). Linear systems (2nd Corrected Printing). Birkhäuser.
   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/https://doi.org/10.1016/j.cam.2008.12.029
   Web of Science ®Google Scholar
• Chahlaoui, Y., & Van Dooren, P. (2002). A collection of benchmark examples for model reduction of linear time invariant dynamical systems. http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf
   Google Scholar
• Chou, J. H., & Horng, I. R. (1986). Simple methods for the shift-transformation matrix, direct-product matrix and summation matrix of discrete Walsh series. International Journal of Control, 43(4), 1339–1342. https://doi.org/https://doi.org/10.1080/00207178608933542
   Web of Science ®Google Scholar
• Feldmann, P., & Freund, R. W. (1995). Efficient linear circuit analysis by Padé approximation via the Lanczos process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(5), 639–649. https://doi.org/https://doi.org/10.1109/43.384428
   Web of Science ®Google Scholar
• Geromel, J. C., Kawaoka, F. R. R., & Egas, R. G. (2004). Model reduction of discrete time systems through linear matrix inequalities. International Journal of Control, 77(10), 978–984. https://doi.org/https://doi.org/10.1080/00207170412331291854
   Web of Science ®Google Scholar
• Ghafoor, A., & Sreeram, V. (2008). Model reduction via limited frequency interval Gramians. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(9), 2806–2812. https://doi.org/https://doi.org/10.1109/TCSI.2008.920092
   Web of Science ®Google Scholar
• Heinkenschloss, M., Reis, T., & Antoulas, A. C. (2011). Balanced truncation model reduction for systems with inhomogeneous initial conditions. Automatica, 47(3), 559–564. https://doi.org/https://doi.org/10.1016/j.automatica.2010.12.002
   Web of Science ®Google Scholar
• Imran, M., & Ghafoor, A. (2014). Stability preserving model reduction technique and error bounds using frequency-limited Gramians for discrete-time systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 61(9), 716–720. https://doi.org/https://doi.org/10.1109/TCSII.2014.2346688
   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/https://doi.org/10.1109/TAC.2011.2161839
   Web of Science ®Google Scholar
• Jiang, Y. L., & Wang, W. G. (2019). Optimal model order reduction of the discrete system on the product manifold. Applied Mathematical Modelling, 69, 593–603. https://doi.org/https://doi.org/10.1016/j.apm.2019.01.012
   Web of Science ®Google Scholar
• Jiang, Y. L., & Xu, K. L. (2021). Frequency-limited reduced models for linear and bilinear systems on the Riemannian manifold. IEEE Transactions on Automatic Control, 66(9), 3938–3951. https://doi.org/https://doi.org/10.1109/TAC.2020.3027643
   Web of Science ®Google Scholar
• Kak, S. (1977). Binary sequences and redundancy. IEEE Transactions on Systems, Man, and Cybernetics, SMC-4(4), 399–401. https://doi.org/https://doi.org/10.1109/TSMC.1974.5408465
   Google Scholar
• Kelley, C. T. (1995). Iterative methods for linear and nonlinear equations. SIAM.
   Google Scholar
• King, R. E., & Paraskevopoulos, P. N. (1977). Digital Laguerre filters. International Journal of Circuit Theory and Applications, 5(1), 81–91. https://doi.org/https://doi.org/10.1002/(ISSN)1097-007X
   Web of Science ®Google Scholar
• Lee, T. T., & Tsay, Y. F. (1986). Application of general discrete orthogonal polynomials to optimal-control systems. International Journal of Control, 43(5), 1375–1386. https://doi.org/https://doi.org/10.1080/00207178608933545
   Web of Science ®Google Scholar
• Mertzios, B. G. (1984). Solution and identification of discrete state-space equations via Walsh functions. Journal of the Franklin Institute, 318(6), 383–391. https://doi.org/https://doi.org/10.1016/0016-0032(84)90045-0
   Web of Science ®Google Scholar
• Mohamed, K. S. (2018). Machine learning for model order reduction. Springer.
   Google Scholar
• Mohseni, S. S., & Khorsand, V. (2019). Design and comparison of ECG arrhythmias classifiers using discrete wavelet transform, neural network and principal component analysis. In M. Hadjiski & K. Atanassov (Eds.), Intuitionistic fuzziness and other intelligent theories and their applications (pp. 181–193). Springer.
   Google Scholar
• Mohseni, S. S, Yazdanpanah, M. J., & Ranjbar Noei, A. (2016). New strategies in model order reduction of trajectory piecewise-linear models. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 29(4), 707–725. https://doi.org/https://doi.org/10.1002/jnm.v29.4
   Web of Science ®Google Scholar
• Mohseni, S. S, Yazdanpanah, M. J., & Ranjbar Noei, A. (2018). Model reduction of nonlinear systems by trajectory piecewise linear based on output-weighting models: A balanced-truncation methodology. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 42(2), 195–206. https://doi.org/https://doi.org/10.1007/s40998-018-0058-4
   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/https://doi.org/10.1109/TAC.1981.1102568
   Web of Science ®Google Scholar
• Mukundan, R., Ong, S. H., & Lee, P. A. (2001). Image analysis by Tchebichef moments. IEEE Transactions on Image Processing, 10(9), 1357–1364. https://doi.org/https://doi.org/10.1109/83.941859
   PubMed Web of Science ®Google Scholar
• Neuman, C. P., & Schonbach, D. I. (1974). Discrete (Legendre) orthogonal polynomials-a survey. International Journal for Numerical Methods in Engineering, 8(4), 743–770. https://doi.org/https://doi.org/10.1002/nme.v8:4
   Google Scholar
• Nikiforov, A. F., Uvarov, V. B., & Suslov, S. K. (1991). Classical orthogonal polynomials of a discrete variable. Springer-Verlag.
   Google Scholar
• Ogata, K. (1995). Discrete-time control systems (2nd ed.). Prentice-Hall.
   Google Scholar
• Penzl, T. (2006). Algorithms for model reduction of large dynamical systems. Linear Algebra and its Applications, 415(2–3), 322–343. https://doi.org/https://doi.org/10.1016/j.laa.2006.01.007
   Web of Science ®Google Scholar
• Qi, Z. Z., Jiang, Y. L., & Xiao, Z. H. (2021). Dimension reduction for k-power bilinear systems using orthogonal polynomials and Arnoldi algorithm. International Journal of Systems Science, 52(10), 2048–2063. https://doi.org/https://doi.org/10.1080/00207721.2021.1876276
   Web of Science ®Google Scholar
• Qu, Z. Q. (2004). Model order reduction techniques with applications in finite element analysis. Springer.
   Google Scholar
• Rewieński, M., & White, J. (2003). A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 22(2), 155–170. https://doi.org/https://doi.org/10.1109/TCAD.2002.806601
   Web of Science ®Google Scholar
• Saad, Y. (2006). Iterative methods for sparse linear systems. SIAM.
   Google Scholar
• Saad, Y., & van der Vorst, H. A. (2000). Iterative solution of linear systems in the 20th century. Journal of Computational and Applied Mathematics, 123(1–2), 1–33. https://doi.org/https://doi.org/10.1016/S0377-0427(00)00412-X
   Web of Science ®Google Scholar
• Shen, J., & Lam, J. (2015). H∞ model reduction for discrete-time positive systems with inhomogeneous initial conditions. International Journal of Robust and Nonlinear Control, 25(1), 88–102. https://doi.org/https://doi.org/10.1002/rnc.v25.1
   Web of Science ®Google Scholar
• Song, Q. Y., Jiang, Y. L., & Xiao, Z. H. (2017). Arnoldi-based model order reduction for linear systems with inhomogeneous initial conditions. Journal of the Franklin Institute, 354(18), 8570–8585. https://doi.org/https://doi.org/10.1016/j.jfranklin.2017.10.014
   Web of Science ®Google Scholar
• Szegö, G. (1975). Orthogonal polynomials (4th ed.). American Mathematical Society.
   Google Scholar
• Tan, S. X. D. (2005). A general hierarchical circuit modeling and simulation algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 24(3), 418–434. https://doi.org/https://doi.org/10.1109/TCAD.2004.842815
   Web of Science ®Google Scholar
• Vasu, G., Siva Kumar, M., & Ramalinga Raju, M. (2021). Internal model control design based on approximation of linear discrete dynamical systems. Applied Mathematical Modelling, 97, 683–700. https://doi.org/https://doi.org/10.1016/j.apm.2021.04.017
   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(13–14), 6650–6662. https://doi.org/https://doi.org/10.1016/j.apm.2016.02.015
   Web of Science ®Google Scholar
• Wang, Z. H., Jiang, Y. L., & Xu, K. L. (2020). Time domain and frequency domain model order reduction for discrete time-delay systems. International Journal of Systems Science, 51(12), 2134–2149. https://doi.org/https://doi.org/10.1080/00207721.2020.1785578
   Web of Science ®Google Scholar
• Zhang, Z. Y., Guo, M. W., & Hesthaven, J. S. (2019). Model order reduction for large-scale structures with local nonlinearities. Computer Methods in Applied Mechanics and Engineering, 353, 491–515. https://doi.org/https://doi.org/10.1016/j.cma.2019.04.042
   Web of Science ®Google Scholar
• Zhou, D., Su, S., Tsui, F., Gao, D. S., & Cong, J. S. (1994). A simplified synthesis of transmission lines with a tree structure. Analog Integrated Circuits and Signal Processing, 5(1), 19–30. https://doi.org/https://doi.org/10.1007/BF01673903
   Web of Science ®Google Scholar