Discrete two-time-scale systems

In this paper reduced-order modelling and control analysis of linear, discrete-time systems having dominant and non-dominant modes are presented. Decoupling of modes is achieved using an explicitly invertible linear transformation. A matrix norm condition is derived, the satisfaction of which enables approximate expressions for the block-diagonalizing matrices, eigenvalue distribution and state trajectories to be obtained. Design of stabilizing feedback controllers is developed and it is shown that two gain matrices are needed for separate assignment of dominant and non-dominant eigenvalues. The theoretical analysis is illustrated by control system examples. © 1986 Taylor & Francis Group, LLC.