International Journal of Systems Science, 2002, volume 33, number 10, pages 847±854 Computation of reduced-order models of multivariable systems by balanced truncation J. S. Garciay and J. C. Basilioz* Previous algorithms to obtain reduced-order models by balanced truncation in a single step either require a very speci®c way to solve a pair of Lyapunov equations or are suitable only for scalar or symmetric MIMO systems. In this paper, model reduction is revisited and an algorithm to obtain a reduced order model in one step only is proposed. As in the previous algorithms, the key point is to construct two rectangular matrices whose smaller dimensions are equal to the number of Hankel singular values to be kept in the lower model. Unlike the one-step algorithms available in the literature, the algorithm proposed here does not make any restriction to the way the Lyapunov equa- tions necessary to obtain the controllability and observability gramians are solved. Furthermore, since the algorithm only relies on singular value decomposition, it is expected to be robust. 1. Introduction Balanced realization (Moore 1981) has been proved crucial in model reduction (Glover 1984) and also in the computation of H 1 optimal controllers in the 1984 approach (Doyle 1984). The idea behind its use in model reduction is to measure the degree of controllability and observability of the system modes and then to discard those modes which are weakly controllable or obser- vable. The computation of reduced-order models by balanced truncation for non-minimal order systems was initially carried out in three steps: (1) computation of a minimal realization for the system; (2) construction of a similarity transformation that relates the state-space realization obtained in step (1) to a balanced realization (Moore 1981, Laub et al. 1987 and references therein); and (3) for a given error bound, balanced truncation is deployed to reduce the system order (Glover 1984). This three-step approach has the drawback that a minimal order realization has to be found whose computation is known to be problematic. To avoid such a di