On the Properties of $\gamma$-.$\varepsilon$ for $H_\infty$ Control by State Feedback and Computation of the Infimum of $H_\infty$ Norm

It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.