On The Non-Fragile Robust Controller Design

Abstract

In the last years the problem of fragile controllers (high sensitivity of closed-loop
stability and/or performance against small changes in controller coefficients) designed by using
robust and optimal control methods has generated some controversial discussions. In this paper,
we analyse the parametric stability margins for some optimal controllers by using different
measures. So, we show that the normalized l^2 parametric stability margin is not suitable when the
controller coefficients lie in very different ranges and, in this case, we propose a new measure to
appreciate the parametric stability margin. Also, we propose some reformulations of optimization
problem such that to increase the parametric stability margins around the coefficients of the
designed optimal controller. An algorithm to determine an extended range of robust stability is
presented. Also, an iterative algorithm that allows computing controllers with increased
parametric stability margins is proposed. We illustrate these design techniques by numerical
examples.