Reformulating negative imaginary frequency response systems to bounded-real systems

This paper provides a reformulation of closed-loop systems that have negative imaginary frequency response to closed-loop systems that have bounded gain, so that theory and results from H_∞ control can be borrowed to enable controller synthesis for the former class of systems. Systems with negative imaginary frequency response arise for example in structures with co-located position sensors and force actuators, and finding a systematic controller synthesis treatment for such systems has important applications in, for example, lightly damped large space structure problems. The key result in this paper assists by reformulating such systems into a bounded-real framework. An example demonstrates the feasibility of the reformulation given herein.