Robustness Margin Calculation with Dynamic and Real Parametric Uncertainty

Abstract

The problem of Robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics where the latter takes the form of one complex block dynamic uncertainty is considered. A robustness margin r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> is defined with respect to such model uncertainty structure and robust stability is characterized in terms of it. An algorithm to calculate r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> and the closely related Multivariable Stability Margin k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> and Structured Singular Value μ measures of Robust Stability is developed. It is shown that other control problems such as robust performance for real parametric uncertainty can also be handled in this framework.