Existence conditions for the stabilizing solution to the time-varying discrete Riccati equation

We present necessary and sufficient conditions together with explicit formulae for the stabilizing solution of the time-varying discrete Riccati equation under no restrictive positivity assumptions on the coefficient matrices. The results are generalization to the time varying case of the matrix pencil type approach of the discrete (time invariant) Riccati equation presented previously by the authors (1995). The results apply to a large class of Riccati equations arising from the disturbance attenuation control problem, quadratic control, maxmin and Nehari problems, or from various factorizations.