Discretetime negative imaginary systems
Abstract
In this paper we introduce the notion of a discretetime negative imaginary system and we investigate its relations with discretetime positive real system theory. In the framework presented here, discretetime negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discretetime positive real functions, as well as analogously to the continuoustime case. This means in particular that we do not need to restrict our notions and definitions to systems with rational transfer functions. We also provide a discretetime counterpart of the different notions that have appeared so far in the literature within the framework of strictly positive real and in the more recent theory of strictly negative imaginary systems, and to show how these notions are characterized and linked to each other. Stability analysis results for the feedback interconnection of discretetime negative imaginary systems are also derived.
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