Revisiting robust stabilization of coprime factors: The general case

Abstract

This article considers the robust stabilization problem of uncertain linear-time invariant plants with coprime factor uncertainty bounded in ℛℋ ∞ . The problem considered here is a generalization of the normalized coprime factor robust stabilization problem. It is shown that the problem admits a simple and intuitive controller implementation parameterized in terms of a state-feedback matrix F and observer gain L. The choice of a state-feedback matrix F induces a metric in which distance between plants is measured. Subsequently, an observer gain L can be obtained to maximize robustness of the controller in this metric via the solution of a Riccati equation. This synthesis method results in a controller of the same order as the nominal plant. It is also shown that non-normalized coprime factorizations are a more suitable tool for obtaining robustly stabilizing controllers for uncertain lightly damped plants than normalized coprime factorizations, which only provide very limited robustness guarantees.