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

A Gramian-based approach to model reduction for uncertain systems

The paper considers the problem of model reduction for a class of uncertain systems with structured norm bounded uncertainty. The paper introduces controllability and observability Gramians in terms of certain parameterized algebraic Riccati inequalities. This enables a balanced trun-cation model reduction procedure for uncertain systems to be presented. Error bounds for this model reduction procedure are derived. The paper also investigates H ∞ model reduction for uncertain systems. The solution to this problem is shown to involve constructing the underlying Gramians satisfying a certain rank constraint. ©2007 IEEE