On Parametric H_infinity Optimization
P. Kabamba and S. Boyd
Proceedings IEEE Conference on Decision and Control, 2:1354-1355, December 1988.
The problem of optimizing the H_infinity norm of a rational transfer matrix with respect to a finite number of design parameters is considered. The H_infinity norm is characterized as a value of a parameter for which a certain Hamiltonian matrix has multiple eigenvalues. A coprimeness test for polynomials is used to characterize the H_infinity norm algebraically as an implicit function of the design parameters. In the case of a single design parameter, necessary conditions for optimality are obtained in the form of a system of two algebraic equations with two unknowns.