Computation of Impulse-Response Gramian for Interval Systems

References

• H. Lu, Z. Cai, Q. Feng, W.-B. Shangguan, and D. Yu, “An improved method for fuzzy-interval uncertainty analysis and its application in brake instability study,” Comput. Method Appl. Mech. Eng., Vol. 342, pp. 142–60, Dec. 2018.
   Web of Science ®Google Scholar
• H. Lu, W.-B. Shangguan, and D. Yu, “A unified method and its application to brake instability analysis involving different types of epistemic uncertainties,” Appl. Math. Modell., Vol. 56, pp. 158–71, Apr. 2018.
   Web of Science ®Google Scholar
• H. Lu, W.-B. Shangguan, and D. Yu, “Uncertainty quantification of squeal instability under two fuzzy-interval cases,” Fuzzy Sets Syst., Vol. 328, pp. 70–82, Dec. 2017.
   Web of Science ®Google Scholar
• H. Lu, W.-B. Shangguan, and D. Yu, “An impreise probability approach for squeal instability analysis based on evidence theory,” J. Sound Vib., Vol. 387, pp. 96–113, Jan. 2017.
   Web of Science ®Google Scholar
• H. Lu, W.-B. Shangguan, and D. Yu, “A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties,” Mech. Syst. Sig. Process., Vol. 93, pp. 281–98, Sep. 2017.
   Web of Science ®Google Scholar
• B. Bandyopadhyay, O. Ismail, and R. Gorez, “Routh-Pade approximation for interval systems,” IEEE Trans. Autom. Control, Vol. 39, no. 12, pp. 2454–6, Dec. 1994.
   Web of Science ®Google Scholar
• B. Bandyopadhyay, A. Upadhye, and O. Ismail, “γ−δ Routh approximations for interval systems,” IEEE Trans. Autom. Control, Vol. 42, no. 8, pp. 1127–30, Aug. 1997.
   Google Scholar
• Y. Dolgin, “Author's reply [to comments on ‘On Routh-Pade model reduction of interval systems’],” IEEE Trans. Autom. Control, Vol. 50, no. 2, pp. 274–5, Feb. 2005.
   Web of Science ®Google Scholar
• Y. Dolgin and E. Zeheb, “On Routh-Pade model reduction of interval systems,” IEEE Trans. Autom. Control, Vol. 48, no. 9, pp. 1610–12, Sep. 2003.
   Web of Science ®Google Scholar
• C. Hwang and S. F. Yang, “Comments on the computation of interval Routh approximants,” IEEE Trans. Autom. Control, Vol. 44, no. 9, pp. 1782–7, Sep. 1999.
   Web of Science ®Google Scholar
• S. F. Yang, “Comments on Routh-Pade approximation for interval systems,” IEEE Trans. Autom. Control, Vol. 50, no. 2, pp. 273–4, Mar. 2005.
   Web of Science ®Google Scholar
• G. V. K. R. Sastry, R. G. Raja, and R. P. Mallikarjuna, “Large scale interval system modelling using Routh approximants,” Elecron. Lett., Vol. 36, no. 8, pp. 768–9, Apr. 2000.
   Web of Science ®Google Scholar
• D. Kranthi Kumar, S. K. Nagar, and J. P. Tiwari, “Order reduction of interval systems using Alpha and factor division method,” Recent Advan. Syst. Modell. Appl., Vol. 188, pp. 249–60, Mar. 2013. Lect. Not. in Elect. Eng., Springer, India.
   Google Scholar
• N. Selvaganesan, “Mixed method of model reduction for uncertain systems,” Serb. J. Electr. Eng., Vol. 4, no. 1, pp. 1–12, Jan. 2007.
   Google Scholar
• M. S. Kumar and B. Gulshad, “A new biased model order reduction for higher order interval systems,” Adv. Electr. Electron. Eng., Vol. 14, no. 2, pp. 145–52, Jan. 2016.
   Web of Science ®Google Scholar
• N. V. Anand, M. S. Kumar, and R. S. Rao, “A novel reduced order modelling of interval system using soft computing optimization approach,” Proc. Inst. Mech. Eng. Part 1: J. Sys. Control Eng., Vol. 232, no. 7, pp. 879–94, Apr. 2018.
   Web of Science ®Google Scholar
• N. S. Tanwar, B. Rajesh, and P. Girish, “Order reduction of interval systems using Big bang Big Crunch and Routh approximation,” in IEEE International Conference on Power Electronics, Intelligent Control and Enery Systems, July 2016, pp. 1–5.
   Google Scholar
• A. K. Choudhary and S. K. Nagar, “Order reduction techniques via Routh approximation: A critical survey,” IETE J. Res., pp. 1–15, Jan. 2018. DOI: 10.1080/03772063.2017.1419836
   Web of Science ®Google Scholar
• S. Afzal and R. Prasad, “A new technique for reduced-order modelling of linear time-invariant system,” IETE J. Res., Vol. 63, no. 3, pp. 316–24, Jan. 2017.
   Web of Science ®Google Scholar
• A. P Kumar and R. Prasad, “Order reduction of linear dynamic systems by improved Routh approximation methos,” IETE J. Res., pp. 1–14, Apr. 2018. DOI: 10.1080/03772063.2018.1452645
   Web of Science ®Google Scholar
• A. P. Kumar and R. Prasad, “Model order reduction by using balanced truncation and factor division methods,” IETE J. Res., pp. 1–16, June 2018. DOI:10.1080/03772063.2018.1464971
   Web of Science ®Google Scholar
• P. Agathoklis and V. Sreeram, “Identification and model reduction from impulse response data,” Int. J. Syst. Sci., Vol. 21, no. 8, pp. 1541–52, 1990.
   Web of Science ®Google Scholar
• Y. Choo and J. Choi, “Properties of a generalized impulse response gramian with application to model reduction,” Int. J. Control Autom. Syst., Vol. 2, no. 4, pp. 516–22, Dec. 2004.
   Web of Science ®Google Scholar
• V. Sreeram and P. Goddard, “Model reduction using impulse response gramians: a frequency-domain approach,” Int. J. Syst. Sci., Vol. 23, no. 10, pp. 1745–59, 1992.
   Web of Science ®Google Scholar
• V. Sreeram and F. K. Yam, “Characteristic impulse response grammians,” Electron. Lett., Vol. 27, no. 14, pp. 1285–7, July 1991.
   Web of Science ®Google Scholar
• V. Sreeram and K. S. Yong, “Evaluation of Gram matrix diagonal elements using inners technique,” Electron. Lett., Vol. 27, no. 12, pp. 1069–71, June 1991.
   Web of Science ®Google Scholar
• Y. Choo and D. Kim, “SISO continuous-system reduction via impulse response gramian by iterative formulae,” J. Dyn. Syst. Meas. Control Autom. Syst., Vol. 128, pp. 391–3, June 2006.
   Web of Science ®Google Scholar
• S. Sahlan, A. Ghafoor, and V. Sreeram, “A new method for the model reduction via a limited frequency interval impulse response gramian,” Math. Comput. Model., Vol. 55, pp. 1034–40, Feb. 2012.
   Google Scholar
• H. R. Shanker, “Upper and lower bonds of frequency interval gramians for a class of perturbed linear systems,” in Proceedings of the 7th IFAC Symposium on Robust Control Design, Aslborg, Jun. 2012, pp. 713–6.
   Google Scholar
• S. Li, Y. Ren, H. Bao, and W. Zhang, “Computation of Gram matrix and its partial derivative using precise integration method for linear time-invariant systems,” J. Appl. Math., pp. 1–10, Mar. 2014.
   Google Scholar
• A. Jazlan, V. Sreeram, R. Togneri, and H. B. Minh, “Generalized gramian based frequency interval model reduction for unstable systems,” in Australian Control Conference, Newcastle, Nov. 2016, pp. 43–7.
   Google Scholar
• A. J. B. Mohideen, “Singular value decomposition based model order reduction techniques,” Ph.D. thesis, School of Elect., Electr. and Comput. Eng., University of Western Australia, Sep. 2016.
   Google Scholar
• A. Jazlan, V. Sreeram, H. R. Shanker, R. Togneri, and H. B. Minh, “Frequency interval cross gramian for linear and bilinear systems,” Asia J. Control, Vol. 19, no. 1, pp. 22–34, Jan. 2017.
   Web of Science ®Google Scholar
• H. R. Shanker and M. Tahavori, “On the existence of frequency-interval gramians for bilinear systems,” Eur. J. Control, Vol. 38, pp. 47–51, Sep. 2017.
   Web of Science ®Google Scholar
• K. S. Haider, A. Ghafoor, M. Imran, and M. F. Mumtaz, “Model reduction of large scale descritor systems using time limited gramians,” Asia J. Control, Vol. 19, pp. 1217–27, Jan. 2017.
   Web of Science ®Google Scholar
• U. Zulfiqar, M. Imran, A. Ghafoor, and M. Liaqut, “A new frequency-limited interval gramians-based model reduction technique,” IEEE Trans. Circ. Syst. II-Exp. Bri., Vol. 64, no. 6, pp. 680–4, June 2017.
   Web of Science ®Google Scholar
• S. Haider, A. Ghafoor, M. Imran, and F. M. Malik, “Frequency interval gramians based structure preserving model order reduction for second order systems,” Asia J. Control, Vol. 20, no. 2, pp. 790–801, Mar. 2018.
   Web of Science ®Google Scholar
• V. L. Kharitonov, “Asymptotic stability of an equilibrium position of a family of system of linear differential equation,” Differ. Equ., Vol. 14, pp. 2086–8, Mar. 1978.
   Google Scholar