Generalized H2 Static Output Feedback Control for Continuous-Time Systems

This paper is concerned with the design problem of generalized H-2 static output feedback (SOF) for continuous-time systems. Due to the fact that SOF control is the simplest closed-loop control and the controller can be easily implemented in practice, the design of SOF controllers has attracted considerable attention. However, analytic solutions were generally given in terms of bilinear matrix inequalities (BMIs). Moreover, how to efficiently solve the BMIs is still a challenging problem. In this paper, a virtual output generator is used such that the states follow the input of the generator. The design of SOF controllers is converted into a design of state feedback controllers. In order to suppress the external disturbance, we adopt the generalized H-2 (energy-to-peak) performance index. Sufficient conditions for the existence of the controller and for the solvability of the addressed problem are given in terms of a set of linear matrix inequalities (LMIs).