Time-varying discrete Riccati equation: l/sup 2/-invertibility, dichotomy, and disconjugacy

Necessary and sufficient existence conditions for the stabilizing solution to the time-varying discrete Riccati equation are given. The result is simply expressed in terms of the original input data via the l/sup 2/-uniformly bounded invertibility of an appropriate family of Toeplitz-like operators. Intimate connections with the notions of dichotomy and disconjugacy are also pointed out. Some aspects concerning the dependence of the existence conditions on the monotonicity of the input data are investigated as well.