2014/12/17 by Augusto Ferrante, Ferrante, Augusto, Alexander Lanzon +3
Computer Science · Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Force Microscopy Techniques and Applications #Iterative Learning Control Systems #Nonlinear Dynamics and Pattern Formation #Piezoelectric Actuators and Control
paper · pdf · doi:10.48550/arxiv.1412.5709
openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we lay the foundations of a not necessarily rational negative\nimaginary systems theory and its relations with positive real systems theory\nand, hence, with passivity. In analogy with the theory of positive real\nfunctions, in our general framework, negative imaginary systems are defined in\nterms of a domain of analyticity of the transfer function and of a sign\ncondition that must be satisfied in such domain. In this way, on the one hand,\nour theory does not require to restrict the attention to systems with rational\ntransfer function and, on the other hand | just by suitably selecting the\ndomain of analyticity to be either the right half complex plane or the\ncomplement of the unit disc in the complex plane | we particularize our theory\nto both continuous-time and to discrete-time systems. Indeed, to the best of\nour knowledge, this is first time that discrete-time negative imaginary systems\nare studied in the literature. In this work, we also aim to provide a unitary\nview of the different notions that have appeared so far in the literature\nwithin the framework of positive real and in the more recent theory of negative\nimaginary systems, and to show how these notions are characterized and linked\nto each other.\n A stability analysis result for the interconnection of discrete-time systems\nis also derived.\n