On the simultaneous stabilisation by static output feedback problem

In this paper, we propose a new algorithmic solution for the simultaneous stabilisation by decentralised static output feedback problem. The addressed problem is considered in its equivalent formulation as a feasibility one involving Bilinear Matrix Inequalities (BMI, for short), which is well known to be very hard to solve. The procedure we describe generates solutions to the original problem by solving a sequence of auxiliary quadratic problems, each one of which is solved by standard methods. As our numerical procedure tends to place some eigenvalues near to the jω-axis, we have included an additional constraint related to pole placement in order to avoid this undesirable feature. Finally, the potential of our scheme is illustrated through two numerical examples.