Alternative derivation of the algebraic Riccati equation in \(\mathcal{H}_ \infty\) control (Q674965)

The full-information \(H_\infty\)-control problem for finite-dimensional linear, time-invariant, continuous-time systems is considered. The well-known solution to the problem is described by the use of algebraic Riccati equations. The purpose of the paper, originally written for students, is to present an alternative proof of the Riccati equation condition obtained by \textit{J. C. Doyle, K. Glover, P. P. Khargonekar} and \textit{B. A. Francis} [IEEE Trans. Autom. Control 34, No. 8, 831-847 (1989; Zbl 0698.93031)]. The given derivation is based on the standard techniques developed for linear control problems formulated in the frequency domain. The paper seems to be helpful, and not only for purely tutorial purposes.