On the strengthened robust SPR problem for discrete-time systems (Q5932280)

It is shown that the solution to the problem of finding conditions for the existence of a rational function \(C(s)\) such that \(C(s)/A(s)-\gamma\) is strictly positive real for all polynomials \(A(s)\) of the convex hull of the polynomials \(A_1(s),\dots, A_r(s)\) is not extensible mutatis-mutandis to the ``discrete-time'' case; i.e. for functions whose positive realness is considered with respect to the unit disk. Moreover, the necessary conditions are \(\gamma\)-dependent (unlike the ``continuous-time case'').