LMI approach to static output feedback simultaneous stabilization of discrete-time interval systems with time delay

The simultaneous static output feedback stabilization problem for a collection of discrete-time interval systems with time delays is considered. A sufficient condition for the existence of static output feedback simultaneously stabilizing controllers is obtained in terms of matrix spectral norms. It is shown that this considered problem is solvable if a corresponding matrix's spectral norm assignment problem is solvable. Furthermore, we also show that the matrix spectral norm assignment problem is equivalent to a bilinear matrix inequality (BMI) problem. We then derive a sufficient condition for the BMI problem and the condition is a linear matrix inequality (LMI) feasibility problem, which can be solved easily. Finally, an example is provided to demonstrate the effectiveness of the proposed methodology.