Abstract
A concept of symmetry for linear systems is defined in terms of input-output relationship. It is shown that there exists a symmetric optimal solution for a symmetric standardH ∞ control problem, as well as for a symmetric model matching problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, State-space solution to standardH 2 andH ∞ control problems. IEEE Trans. Automat. Control,AC-34 (1989), 831–847.
B.A. Francis and J.C. Doyle, Linear control theory with anH ∞ optimality criterion. SIAM J. Control Optim.,25 (1987), 815–844.
J.W. Grizzle and S.I. Marcus, The structure of nonlinear control systems possessing symmetries. IEEE Trans. Automat. Control,AC-30 (1985), 248–257.
T. Kailath, Linear Systems. Prentice-Hall, NJ, 1980.
V. Kučera, A Contribution to matrix quadratic equations. IEEE Trans. Automat. Control,AC-17 (1972), 344–347.
K. Murota, Hierarchical decomposition of symmetric discrete systems by matroid and group theories. Math. Programming, Ser. A, to appear.
H. Nijmeijer and A.J. van der Schaft, Partial symmetry for nonlinear systems. Math. Systems Theory,18 (1985), 79–96.
J.-P. Serre, Linear Representations of Finite Groups. Springer-Verlag, 1977.
A.J. van der Schaft, Symmetries and conservation laws for Hamiltonian systems with inputs and outputs: A generalization of Noether’s theorem. Systems Control Lett.,1 (1981), 108–115.
Author information
Authors and Affiliations
About this article
Cite this article
Iwata, S. H ∞ optimal control for symmetric linear systems. Japan J. Indust. Appl. Math. 10, 97–107 (1993). https://doi.org/10.1007/BF03167205
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03167205