The Extended Generalized Distance Problem in Discrete Time

Abstract

We obtain the class of all solutions to the extended (two block) generalized distance problem for discrete-time systems by employing the so-called 'signature condition' - a generalized Popov theory type argument which parallels the J-spectral factorization approach. The novelty is that we derive explicit state-space formulae in terms of one Riccati and one Lyapunov equation while we remove the usual assumption in the discrete case on the time reversibility (invertibility of the state matrix) of the system to be approximated.