Liu, Yi; Anderson, Brian D. O. Frequency weighted controller reduction methods and loop transfer recovery. (English) Zbl 0714.93015 Automatica 26, No. 3, 487-497 (1990). Summary: This paper shows that if one designs an LQG controller using the conventional technique of loop transfer recovery (LTR), then two frequency weighted controller reduction methods, the Enns’ frequency weighted balanced truncation [see D. F. Enns, “Model reduction for control systems design”, Ph.D. Thesis, Dep. Aeronatu. Astronaut., Stanford Univ./Calif. 1984; “Model reduction with balanced realizations”, Proc. 23rd IEEE Conf., Decis. Control, Las Vegas/NV (USA) 1984, Vol. 1, 127-132 (New York 1984)] and the Bezout identity induced frequency weighted reduction method [the authors, “Controller reduction: Concepts and approaches”, Proc. 1987 Am. Control Conf., Minneapolis/MN 1987, Vol. 1, 1-9 (Piscataway/NJ 1987); see also IEEE Trans. Autom. Control 34, No.8, 802-812 (1989; Zbl 0698.93034)] will be equivalent under the condition that the plant transfer function is square, nonsingular and minimum phase. We also show that Enns’ method is equivalent to the Bezout identity induced frequency weighted reduction method if the controller itself is stable and a particular representation for the controller is assumed. Cited in 2 Documents MSC: 93B50 Synthesis problems 93B11 System structure simplification 49N05 Linear optimal control problems 49N70 Differential games and control 49N75 Pursuit and evasion games Keywords:LQG controller; loop transfer recovery (LTR); frequency weighted controller reduction methods; frequency weighted balanced truncation; Bezout identity induced frequency weighted reduction method Citations:Zbl 0698.93034 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{B. D. O. Anderson}, Automatica 26, No. 3, 487--497 (1990; Zbl 0714.93015) Full Text: DOI References: [1] Al-Saggaf, U. M.; Franklin, G. F., On model reduction, (Proc. 25th CDC. Proc. 25th CDC, Athens, Greece (1986)) [2] Anderson, B. D.O., Weighted Hankel norm approximation: Calculation of bounds, Syst. Control Lett., 7, 247-255 (1986) · Zbl 0595.93024 [3] Anderson, B. D.O.; Liu, Y., Controller reduction: Concepts and approaches, (Proc. Amer. Control Conf.. Proc. Amer. Control Conf., MN (1987)) · Zbl 0629.93035 [4] Anderson, B. D.O.; Moore, J. B., (Linear Optimal Control (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, N J) [5] Doyle, J. C.; Stein, G., Robustness with observers, IEEE Trans. Aut. Control, AC-24, 607-611 (1979) · Zbl 0412.93030 [6] Doyle, J. C.; Stein, G., Multivariable feedback design: concepts for a classical/modern systhesis, IEEE Trans. Aut. Control, AC-26, 4-16 (1981) · Zbl 0462.93027 [7] Enns, D. F., Model reduction for control systems design, (Ph.D. Thesis (1984), Department of Aeronautics and Astronautics, Stanford University: Department of Aeronautics and Astronautics, Stanford University CA) [8] Enns, D. F., Model reduction with balanced realizations: An error bound and a frequency weighted generalization, (Proc. 23rd CDC. Proc. 23rd CDC, Las Vegas, NV (1984)), 127-132 [9] Francis, B. A., The optimal linear-quadratic time-invariant regulator with cheap control, IEEE Trans. Aut. Control, AC-24, 616-621 (1979) · Zbl 0424.49022 [10] Kwakernaak, H.; Sivan, R., (Linear Optimal Control Systems (1972), Wiley Interscience: Wiley Interscience New York) · Zbl 0276.93001 [11] Latham, G. A.; Anderson, B. D.O., Frequency-weighted optimal Hankel norm approximation of stable transfer functions, Syst. Control Lett., 5, 229-236 (1985) · Zbl 0559.93036 [12] Liu, Y.; Anderson, B. D.O., Controller reduction via stable factorization and balancing, Int. J. Control, 44, 507-531 (1986) · Zbl 0604.93020 [13] Liu, Y.; Anderson, B. D.O.; Ly, U.-L., Coprime factorization controller reduction with Bezout identity induced frequency weighting, Automatica, 26, 233-249 (1990) · Zbl 0708.93029 [14] Nett, C. N.; Jacobson, C. A.; Balas, M. J., A connection between state-space and doubly coprime fractional representations, IEEE Trans. Aut. Control, AC-29, 831-832 (1984) · Zbl 0542.93014 [15] Vidyasagar, M., (Control System Synthesis: A Factorization Approach (1985), MIT Press: MIT Press Cambridge, MA) · Zbl 0655.93001 [16] Yousuff, A.; Skelton, R. E., A note on balanced controller reduction, IEEE Trans. Aut. Control, AC-29, 254-256 (1984) · Zbl 0535.93014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.