An explicit formula for general H∞ control

This paper extends the result of M.C. Tsai and C.S. Tsai (see IEEE Trans. Automat. Contr., vol.38, p.1416-21, 1993) to a general H^∞ control problem which only requires the stabilizing assumption on the generalized plant. By introducing coprime factors of the plant, the necessary and sufficient conditions for the existence of a sub-optimal solution are derived completely in the transfer function domain. The solution is obtained via finding a J-contractive and a J-expansive numerator, respectively, of two associated factorizations; this is equivalent to the existence of positive definite solutions of two corresponding Riccati inequalities in the state-space. The aim of the present paper provides a linkage between J-contractive factorizations and linear matrix inequalities, and an explicit state-space formula for constructing H^∞ controllers