Convex Synthesis of Strictly Negative Imaginary Feedback Controllers

This paper presents linear matrix inequality approaches to optimally synthesize strictly negative imaginary (SNI) dynamic output feedback controllers. In particular, convex controller synthesis methods are introduced that minimize either the weighted H₂ or H_∞ norm of the difference between a specified optimal controller and the synthesized SNI controller. Numerical examples are included that demonstrate the performance and robustness of the proposed synthesis methods when used for the vibration control of an Euler-Bernoulli beam.