An algebraic approach to analysis and control of timescales

The structure of time-scales in systems of the form x = A(S)x is related to the invariant factors of A(M) when this matrix is over the ring of functions analytic at 0. This relationship motivates the study of invariant factor assignment in the matrix A(C) + B(S) K(£) by choice of K(g). Results on this problem have implications for assignment of time-scales by state feedback in systems of the form x = A(C)x + B(c)u. Work in this direction is presented