Kanghong Shi's Talk on Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

Title: Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

Time, Date, Location: 11:00, Friday, 24 February, 2023, Brian Anderson Building Seminar Room

Abstract: We present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. Then we apply the NI state feedback equivalence result to robustly stabilize an uncertain system with strictly negative imaginary uncertainty. A real-world example is provided to illustrate the proposed results, for the purpose of stabilizing an uncertain system.