Analytical formulation to compute QFT bounds: The envelope method

This paper describes an analytical formulation to compute quantitative feedback theory (QFT) bounds in one-degree-of-freedom feedback control problems. The new approach is based on envelope curves and shows that a QFT control specification can be expressed as a family of circumferences. Then, the controller bound is defined by the envelope curve of this family and can be obtained as an analytical function. This offers the possibility of studying the QFT bounds in an analytical way with several useful properties. Gridding methods are avoided, resulting in a lower computational effort procedure. The new formulation improves the accuracy of previous methods and allows the designer to calculate multivalued bounds. Copyright (C) 2009 John Wiley & Sons, Ltd.