J-inner outer factorization for bilinear systems

This article gives formulas for two factors of a given bilinear system. One factor is lossless and the other is stable with stable inverse. Such are called J-inner and outer factors, and this article gives conditions insuring such factors exist. It specializes very high level formulas announced in Helton and James (1994) for general nonlinear systems with the result that we obtain rather concrete formulas. Also it proves theorems about the factors which are stronger than those of Helton and James. In linear H_∞ control producing J-inner outer factors of a given system leads directly to the usual linear fractional parameterization of all solutions to the H_∞ control problem. Indeed this powerful parameterization is equivalent to such a factorization. For nonlinear systems such factors parametrize many solutions to the H_∞ control problem, but whether it parameterizes all solutions is not known. This article develops Helton and James´ article which gave formulas for and conditions for checking existence of such factors when the system to be factored is stable