Synthesis of simultaneous stabilizing H∞ Controller controller

In the chain scattering framework, it has been shown in Lee and Soh (2004) that the problem of simultaneous stabilization of a finite collection of l linear time-invariant plants such that each closed-loop transfer function has an norm less than a prescribed performance level is equivalent to a simultaneous strongly stabilizing problem, i.e. finding a single stable and norm bounded controller for associated l − 1 unimodular plants such that each resulting closed-loop system is stable and norm bounded. This paper attempts to provide a solution to the simultaneous strongly stabilization problem. A new sufficient condition in the form of the solution to only one algebraic Riccati equation is provided for the existence of a strongly stabilizing controller for a given stable system obtained from the parameterization of stabilizing controllers. With the parameterization of strongly stabilizing controllers provided in this paper, a solution is given for the simultaneous strongly stabilization problem and hence, ...