Model reduction of complex systems in the linear-fractional framework

This paper discusses model reduction for systems in several different classes, in particular time-varying, multidimensional or uncertain systems, and nonlinear systems in the linear-fractional framework. We describe in detail the unifying viewpoint that this framework provides to all of these classes, and discuss the numerical methods used to construct reduced-order models. The methods used are extensions of the well-known method of balanced truncation, with provably good properties in the induced-norm.