Static Output Feedback Control of Discrete-Time Linear Systems: Background Results and New LMI Conditions

In this paper, attention is focused on the design of a stabilizing static output feedback (SOF) gain matrix for linear discrete-time systems. Our design methodology of the SOF controller is based on the linear matrix inequality (LMI) approach. Unlike the state feedback control case, the SOF formulation usually leads to non-convex stability conditions, which are expressed in terms of Bilinear Matrix Inequalities (BMIs) that are not numerically traceable. To circumvent the computation problem of the SOF gain, several techniques have been developed to transform the non-convex conditions into convex ones. In this paper, some background results related to this convexity problem are firstly presented. Furthermore, a new approach is employed in this work to transform the BMI constraints into LMIs by introducing a new lemma. Finally, a simulation example is given to testify the validity of the developed LMI conditions.