Abstract
H∞. control design is generally performed iteratively. At each iteration, the weights constraining the desired closed loop transfer functions are adapted. The way in which the weights are adapted is generally purely heuristic. It is consequently very interesting to build some insights about the influence of a weight modification on the obtained (central) controller and, more importantly, on the obtained closed-loop transfer functions. In this paper, we analyze this influence in the case of a classical two-block problem under the assumption of “small” modifications in the weights. The concept small modificationmust be understood in the sense of small enough to allow first order approximation.
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References
G. Ferreres and V. Fromion, “Computation of the robustness margin with the skewed µ-tool,”Systems Control Lettersvol. 32, pp. 193–202, 1997.
K. Glover and J. C. Doyle, “State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to risk sensitivity,”Systems Control Lettersvol. 11, pp. 167–172, 1988.
M. Green, K. Glover, D. Limebeer, and J. Doyle, “A J-spectral factorization approach toH∞ control,”SIAM Journal on Control and Optimizationvol. 28, no. 6, pp. 1350–1371, 1990.
V. Ionescu and R. Stefan, “Chain-scattering solution to the -y-DF problem: a Popov function approach,”IMA Journal of Mathematical Control and Informationvol. 17, pp. 147–165, 2000.
H. Kimura, “Directional interpolation approach toH∞„optimization and robust stabilization,”IEEE Transactions on Automatic Controlvol. 32, pp. 1085–1093, 1987.
H. Kimura, “Conjugation, interpolation and model-matching inH∞” International Journal of Controlvol. 49, pp. 269–307, 1989.
H. KimuraChain-Scattering Approach to H∞-Control.Boston: Birkhäuser, 1997.
G. Zames, “Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses,”IEEE Transactions on Automatic Controlvol. AC-26, no. 2, pp. 301–320, April 1981.
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Anderson, B.D.O., Bombois, X. (2003). Analysis of Weight Change in H∞Control Design. In: Hashimoto, K., Oishi, Y., Yamamoto, Y. (eds) Control and Modeling of Complex Systems. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0023-9_8
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DOI: https://doi.org/10.1007/978-1-4612-0023-9_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6577-1
Online ISBN: 978-1-4612-0023-9
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