Analytic stabilization and the algebraic Riccati equation

The central result of this paper is that the stabilizing solution P*, to the Algebraic Riccati Equation in (A,B,C) depends analytically on (A,B,C). A variant of this result was first presented in an earlier paper ([13]) by the author, but the simplicity of the proof was obscured by the context; moreover, the version given in ??1 is more general. In addition, ??1 contains recursive formulas for the terms in the Taylor series expansion of P* about a point (A,B,C). In the remainder of the paper, various control - and system-theoretic ramifications of the analyticity lemma are considered.