A sufficient condition for arbitrary eigenvalue assignment in linear descriptor systems by output feedback

The problem of eigenvalue assignment in the linear descriptor system Eẋ = Ax + Bu, y = Cx via output feedback is considered. It is shown that mp> rank(E) (m and p are respectively the numbers of inputs and outputs of the system) is a sufficient condition for generic real output feedback eigenvalue assignability. The result is the best possible for general m, p, rank(E). In general, the assignment is achieved not in an exact sense, but in arbitrarily small neighborhoods around a given set of eigenvalues.