Static output feedback negative imaginary controller design with H₂ performance

In this paper, the problem of designing static output feedback (SOF) H₂ negative imaginary controller has been studied. Because the constraints brought by negative imaginary (NI) property and H₂ performance are a set of bilinear matrix inequalities (BMIs), designing an SOF NI controller with H₂ performance is a non-trivial problem. To overcome the difficulty of solving BMIs, a linearisation-based method is proposed. First, a necessary and sufficient condition is established, where the constraints of NI property and H₂ performance are reformulated as similar forms. Second, inspired by the semidefinite programming, the derived condition is converted to the difference between two convex functions. Then a linearised iterative algorithm with initialisation process is provided to compute the desired SOF H₂ NI controller. Finally, two numerical examples are presented to illustrate the proposed results.