Negative Imaginary Reset Control Systems

In this note, we present an extension of the nonlinear negative imaginary (NI) systems theory to reset systems. We define the reset NI and reset strictly NI systems and provide a state-space characterization of these systems in terms of linear matrix inequalities. Subsequently, we establish the conditions for the internal stability of a positive feedback interconnection of a (strictly) NI linear time-invariant plant and a reset (strictly) NI controller. The applicability of the proposed method is demonstrated in a numerical example of a reset version of a positive position feedback controller for a plant with resonance.