Time-varying discrete Riccati equation in terms of Ben Artzi-Gohberg dichotomy

AbstractNecessary and sufficient conditions for the existence of the stabilizing solution to the time-varying discrete Riccati equation are derived in terms of the so-called Ben Artzi-Gohberg dichotomy. It is shown that the problem of such existence conditions is strongly related to that of unique solvability, in vector-valued l2-spaces, of a system of singular difference equations which, in this case, is termed the extended Hamiltonian system (EHS). Connections between the existence of the stabilizing solution to the Riccati equation and the bounded invertibility of an appropriate l2-operator are pointed out via the notion of disconjugacy