Reduced order modelling and control of two-time-scale discrete systems†

A class of linear shift-invariant discrete systems satisfying a two-time-scale property is defined and a model satisfying this property is given. A pair of explicitly invertible block diagonalizing transformations are used to obtain reduced order fast and slow models analogous to the continuous singularly perturbed case. A deadbeat approximation to the fast modes results in a reduced order slow model, and a ‘ boundary layer ’ error in the original fast states. For control law design, the dual nature of these block diagonalizing transformations allows partial or total eigenvalue placement for fast and/or slow modes based on feedback designs for the reduced order slow and fast models.