A Novel Scheme for Positive Real Balanced Truncation

Here, model reduction, based on balanced truncation, of stable and passive systems will be considered. An overview over some of the already existing techniques will be given; Lyapunov balancing, Riccati balancing and Stochastic balancing. Subsequently a novel scheme for positive real balanced truncation will be proposed. This new method is a combination of the already existing Lyapunov balancing and Riccati balancing. Using Riccati balancing, the solution of two Riccati equations are needed to obtain passive reduced order systems. For the suggested method, only one Lyapunov equation and one Riccati equation are solved in order to obtain passive reduced order systems, which is less computationally demanding. A numerical example is given at the end to compare the approximation error of the different schemes.