H∞ control with weighting functions having purely imaginary poles—implementing internal models toH∞ controllers

Abstract

The present paper considers a variant of the standard H∞ control problem which allows one to use weighting functions having jω poles. Using the solution, one can design H∞ controllers having prescribed jω poles such as internal models. To solve the problem, the authors propose a new requirement of closed-loop stability, called essential stability, and alternative standing assumptions imposed on the generalized plant. To write the results in the form of the so-called 2-ARE solution, the authors introduce the notion of quasi-stabilizing solutions to the algebraic Riccati equations arising in H∞ control. The solution involves the same Riccati equations and parametrization of the controllers given by Glover and Doyle except the stability requirement on the solutions to the Riccati equations.