Abstract
New parametric equations for H ∞-controllers that suppress external perturbations in a given ratio for a linear dynamic object are derived. They do not contain the solutions of matrix equations or inequalities, but are parametrized by linearly contained parameters that take values in a domain defined by two frequency conditions.
Similar content being viewed by others
REFERENCES
Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A., State-Space Solution to Standard H 2 and H ∞ control problems, IEEE Trans. Autom. Control, 1989, vol. 34, no.8, pp. 831-847.
Zhou, K., On the Parametrization of H ∞ Controllers, IEEE Trans. Autom. Control, 1992, vol. 37, no.9, pp. 1442-1446.
Mita, T., Liu, K.Z., and Ohuchi, S., Correction of the FI result in H ∞ Control and Parametrization of H ∞ State Feedback Controllers, IEEE Trans. Autom. Control, 1993, vol. 38, no.2, pp. 343-347.
Gahinet, P. and Apkarian, P., A Linear Matrix Inequality Approach to H ∞ Control, Int. J. Robust Nonlin. Control, 1994, vol. 4, pp. 421-448.
Iwasaki, T. and Skelton, R.E., All Controllers for the H ∞ Control Problem: LMI Existence Conditions and State Space Formulas, Automatica, 1994, vol. 30, no.8, pp. 1307-1317.
Kogan, M.M., Solution to Inverse Problems on the Worst Perturbation and Minimax Control for Linear Continuous-Time Systems, Avtom. Telemekh., 1997, no. 4, pp. 22-30.
Kogan, M.M., Solution to the Inverse Problem of Minimax Control and Worst Case Disturbance for Linear Continuous-Time Systems, IEEE Trans. Autom. Control, 1998, vol. 43, pp. 670-674.
Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost' nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with a Nonunique Equilibrium State), Moscow: Nauka, 1978.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kogan, M.M. A New Parametrization of H ∞-Controllers. Automation and Remote Control 64, 1287–1300 (2003). https://doi.org/10.1023/A:1025031400682
Issue Date:
DOI: https://doi.org/10.1023/A:1025031400682