Simultaneous static output-feedback stabilisation for discrete-time interval systems with time delay

The simultaneous static output-feedback stabilisation problem for a collection of discrete-time interval systems with time delays both in states and in control input is considered. A sufficient condition for the existence of static output-feedback simultaneously stabilising controllers is obtained in terms of matrix spectral norms. It is shown that this problem is solvable if a corresponding matrix spectral norm assignment problem is solvable. It is also shown that the matrix spectral norm assignment problem is equivalent to a bilinear matrix inequality (BMI) problem. A sufficient condition for the BMI problem is then derived and the condition is a linear matrix inequality feasibility problem, which can be solved easily. An example is provided to demonstrate the effectiveness of the proposed methodology.