Efficient Numerical Model Reduction Methods For Discrete-Time Systems

. Model reduction is of fundamental importance in many modeling and control applications. Here we address algorithmic aspects of model reduction methods based on balanced truncation of linear discrete-time systems. The methods require the computation of the Gramians of the system. Using an accelerated fixed point iteration for computing the full-rank factors of the Gramians yields some favorable computational aspects, particularly for non-minimal systems. The computations only require efficient implementations of basic linear algebra operations readily available on modern computer architectures. Introduction Consider the transfer function matrix (TFM) G() = C(I \Gamma A) \Gamma1 B+D, and the associated stable, but not necessarily minimal, realization of a discrete, linear time-invariant (LTI) system, x k+1 = Ax k +Bu k ; y k = Cx k +Du k ; k = 0; 1; 2; : : : ; (1) where x 0 = x is given and A 2 R n\Thetan , B 2 R n\Thetam , C 2 R p\Thetan , D 2 R p\Thetam . The number of ..