Properties and stability analysis of discrete-time negative imaginary systems

This paper is concerned with discrete-time negative imaginary (DT-NI) functions. First, a new definition of DT-NI functions is introduced. Then, by means of the relations between discrete-time positive real and DT-NI functions, two different versions of DT-NI lemmas are established to characterize the DT-NI properties based on state-space realizations. Also, a necessary and sufficient condition is presented to guarantee the internal stability of positive feedback interconnected DT-NI systems. Meanwhile, some other properties of DT-NI functions are studied. Several numerical examples are presented to illustrate the main results of this paper. Compared to the previous results, our results remove the symmetric assumption in rational case.