Simulation of complex systems in terms of simple models with guaranteed error

The simulation of the input output behaviour of a complex multivariable continuous system in terms of a lower order discrete time model is considered. The system and the model are assumed to be linear, asymptotically stable and time invariant. The norm approach is developed and a performance index, which is a bound for a whole class of possible errors in the worst case is minimized with respect to the model parameters. In this way a model is achieved which is well suited for a fast digital simulation and allows the user to compute on line the error bound, together with the simulated output.