Control Theory on the Infinite Dimensional Space

The theory of H-spaces and the H control theory on finite dimensional spaces have been summarized by C. G. Hu and C. C. Yang (Hu and Yang, 1992), and B. A. Francis and J. C. Doyle ((Francis, 1987), (Francis and Doyle, 1987)) respectively. In 1993, B. V. Keulen extended the H control theory on finite dimensional spaces to range in the infinite dimensional Hilbert space (Keulen, 1993). In 2002, C. G. Hu and L. X. Ma extended the result of Keulen to the locally convex space containing the Hilbert space (Hu and Ma, 2002). In this article, the V H control theory on an infinite dimensional algebra to itself is presented in Section 4. For this aim, the meromorphic mapping (in Section 2) and the theory of V H spaces on an infinite dimensional algebra without appearance in books ((Dineen, 1981) and (Mujica, 1986)) respectively, are given (in Section 3). The V H control theory can enlarge the scope of solutions in the control theory. So the research on these problems can develop and complete the control theory.