Output strictly negative imaginary systems and its connections to dissipativity theory

This paper generalises the notion of output strictly negative imaginary systems and provides a complete characterisation both in frequency domain and time domain. The paper also reveals the missing link between the negative imaginary theory and dissipativity. A new time domain supply rate is introduced to characterise the class of output strictly negative imaginary systems that consists of input to the system, the derivative of an auxiliary output of the system and a real parameter δ > 0. Further, in addition to the output strictly negative imaginary systems, all stable negative imaginary systems are shown to be dissipative with respect to the same supply rate with δ =0. An equivalence is also established between the output strictly negative imaginary systems property and time domain dissipativity of this class of systems with respect to the proposed supply rate and a specific positive definite storage function. Several numerical examples are studied to elucidate the essence of the theoretical developments.