A Gramian-based approach to model reduction for uncertain systems

Abstract

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.