Strong stability of discrete-time systems

Halikias, G., Dritsas, L., Pantelous, A. & Tsoulkas, V. (2012). Strong stability of discrete-time systems. Linear Algebra and its Applications, 436(7), pp. 1890-1908. doi: 10.1016/j.laa.2011.09.024

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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.

Item Type: Article
Additional Information: © 2012, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: Discrete-time systems; Strong stability; Non-overshooting response; Eigen-frame skewness; Quadratic stability; Linear Matrix Inequalities (LMI’s); State/output feedback
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/14863

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