On the strengthened robust SPR problem for discrete-time systems

The well-known necessary and su$cient condition to "nd a solution to the robust strictly positive real (SPR) problem, namely, that the phase di!erence of the polynomials involved must be less than p, was found to be also necessary and su$cient in the strengthened robust SPR problem by Anderson and Landau in a recent work, only for the continuous-time case. In this brief communication, we derive a necessary condition in the discrete-time case, which cannot be formulated in phase terms, and which is more stringent than the condition of the robust SPR problem, thereby establishing a fundamental di!erence between both continuous-time and discrete-time domains. ( 2001 Elsevier Science Ltd. All rights reserved.