Stable Fixed Point Assignment Problems in Dynamical Systems and Application to Associative Memory

This paper studies in the framework of systems and control theory with the problem of constructing a dynamical system defined over a Hilbert space such that any given vectors in the Hilbert space are assigned to locally asymptotically stable fixed points of the system. First, introducing a system satisfying the required condition, it is shown that all the assigned fixed points are locally asymptotically stable, and further some important properties of the resultant system are derived. Then, the result is applied for implementing associative memory of two-dimensional images and a new method for handling images corrupted by deformation and nose is studied. Finally, some numerical examples are presented to illustrate the result