Static output feedback negative imaginary controller design with H ₂ performance

Abstract

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.