Computation of reduced-order models of multivariable systems by balanced truncation

Abstract

Previous algorithms to obtain reduced-order models by balanced truncation in a single step either require a very specific 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 equations 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.