Foundations of negative imaginary systems theory and relations with positive real systems
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In this paper we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory and, hence, with passivity. In analogy with the theory of positive real functions, in our general framework, negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain. In this way, on the one hand, our theory does not require to restrict the attention to systems with rational transfer function and, on the other hand | just by suitably selecting the domain of analyticity to be either the right half complex plane or the complement of the unit disc in the complex plane | we particularize our theory to both continuous-time and to discrete-time systems. Indeed, to the best of our knowledge, this is first time that discrete-time negative imaginary systems are studied in the literature. In this work, we also aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems, and to show how these notions are characterized and linked to each other. A stability analysis result for the interconnection of discrete-time systems is also derived.
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Ferrante, A.; Lanzon, A.; Ntogramatzidis, Lorenzo (2017)In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive real system theory. In the framework presented here, discrete-time negative ...
Foundations of not necessarily rational negative imaginary systems theory: relations between classes of negative imaginary and positive real systems. IEEE Transactions on Automatic ControlFerrante, Augusto; Lanzon, A.; Ntogramatzidis, Lorenzo (2016)In this technical note we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory. In analogy with the theory of positive real functions, in ...
Some new results in the theory of negative imaginary systems with symmetric transfer matrix functionFerrante, A.; Ntogramatzidis, Lorenzo (2013)This note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of ...