Strongly (J,J′)‐lossless rational matrices and ℋ∞ problem

We strengthen the existing definition of (J,J′)‐lossless rational matrices (RMs) and find an algebraic characterization of the newly defined class of strongly (J,J′)‐lossless RMs. The algebraic characterization is given for possibly improper RMs. A connection is presented to a rational ? _∞ problem, known as the Leech problem, which is elaborated on with necessary and sufficient conditions, given in terms of the strongly (J,J′)‐lossless property, as an alternative of the Leech conditions, which can be expressed with positivity of a kernel. An algorithm for solving the Leech problem is given and illustrated by examples.