Strong simultaneous stabilization problem using Linear Matrix Inequalities

In this paper, the strong simultaneous stabilization problem for a collection of continoustime systems is considered. A sufficient condition for the existence of dynamic stable controller that stablize a single plant or simultaneously stabilizing a set of plants is obtained in terms of Linear Matrix Inequalities or Quadratic Matrix Inequalities. It is shown that these considered problems are solvable if a corresponding linear matrix inequality (s) are solvable. Furthermore, we derive a sufficient condition for the QMI problem to be solvable.