Optimal triangular approximation for linear stable multivariable systems

This paper deals with the problem of obtaining a stable triangular approximation for a linear, square, stable, discrete-time MIMO system. We solve this problem through an analytic procedure that yields an explicit solution of a convex optimization problem. The optimized quantity is the L₂ norm of the relative modelling error. An interesting feature of the proposed methodology is that, if the MIMO system has nonminimum phase zeros near the stability boundary, then the derived approximation has, at least, a set of zeros close to them. The usefulness of our result comes mainly from its use as nominal model in triangular controller design procedures based on a triangular plant model.