On positive realness and negative imaginariness of uncertain discrete-time state-space symmetric systems

Mei Liu, James Lam, Bohao Zhu and Xingjian Jing

International Journal of Systems Science, 2020, vol. 51, issue 8, 1406-1417

Abstract: This paper provides an analysis of uncertain discrete-time negative imaginary and positive real systems with state-space symmetry. First, a necessary and sufficient condition is provided for a minimal state-space symmetric system to be discrete-time positive real or discrete-time negative imaginary. Then, based on the discrete-time symmetric negative imaginary and positive real lemmas, bounds on symmetrically structured perturbations that maintain the negative imaginariness and positive realness of a discrete-time state-space symmetric system are derived. Finally, an RL network example is provided to illustrate the main results of the paper.

Date: 2020
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DOI: 10.1080/00207721.2020.1764129

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