Characterization of Input–Output Negative Imaginary Systems in a Dissipative Framework

In this article, we define the notion of stable input–output negative imaginary (IONI) systems. This new class captures and unifies all existing subclasses (NI) systems is capable distinguishing between strict (e.g., strongly strictly imaginary, output (OSNI), input etc.) in literature. addition to a frequency-domain definition, proposed IONI has been characterized time-domain dissipative framework terms quadratic supply rate $w(u,\bar{u},\dot{\bar{y}})$ . consists system’s ( notation="LaTeX">$u$ ), an auxiliary notation="LaTeX">$\bar{u}$ ) that filtered version input, time-derivative system notation="LaTeX">$\dot{\bar{y}}$ ). corrects earlier attempts literature, which were only expressed notation="LaTeX">$\dot{y}$ are proved be with respect Subsequently, equivalent frequency-dependent notation="LaTeX">$(Q(\omega), S(\omega), R(\omega))$ also for These findings reveal connections NI property classical dissipativity both time domain frequency domain. We provide linear matrix inequality (LMI) tests on state-space matrices check whether belongs or any its important subclasses. Finally, derived results specialized OSNI since such exhibit interesting closed-loop stability properties when connected, positive feedback loop, without poles at origin. Several illustrative numerical examples provided make intuitive useful.