Abstract
The paper introduces a new notion of stability for internal (state-space) autonomous system descriptions in discrete-time, referred to as strong stability which extends a parallel notion introduced in the continuous-time case. This is a stronger notion of stability compared to alternative definitions (asymptotic, Lyapunov), which prohibits systems described by natural coordinates to have overshooting responses for arbitrary initial conditions in state-space. Three finer notions of strong stability are introduced and necessary and sufficient conditions are established for each one of them. The class of discrete-time systems for which strong and asymptotic stability coincide is characterized and links between the skewness of the eigen-frame and the violation of strong stability property are obtained. Connections between the notions of strong stability in the continuous and discrete-domains are briefly discussed. Finally strong stabilization problems under state and output feedback are studied. The results of the paper are illustrated with a numerical example.
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Summary
This is the other version of the paper. This version of the publication may differ from the final published version. Copyright: City Research Online aims to make research outputs of City, University of London available to a wider audience. URLs from City Research Online may be freely distributed and linked to. Reuse: Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way
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