Controller parametrization and pole-placement design for simultaneous stabilization

The authors investigate the use of stable inversion to obtain nonswitching controllers for the simultaneous stabilization of systems with multiple operating conditions. In a previous work (1990) the authors required the high-frequency gains of the models of the different operating conditions to satisfy a full rank condition. In this paper they remove that constraint and consider general system models, including strictly proper models. A parametrization in terms of a stable inverse system and a stable annihilator system is proposed for all simultaneously stabilizing controllers. Several examples are used to illustrate pole-placement design using proper controllers and strictly proper controllers, and the constraints on the pole-placement design