Complexity Reduction for Parameter-Dependent Linear Systems

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., H-infinity-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples

emgr - The Empirical Gramian Framework

System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramian are an extension to the system Gramians for parametric and nonlinear systems as well as a data-driven method of computation. The empirical Gramian framework - emgr - implements the empirical Gramians in a uniform and configurable manner, with applications such as Gramian-based (nonlinear) model reduction, decentralized control, sensitivity analysis, parameter identification and combined state and parameter reduction