Regions of exponential stability in coefficient space for linear systems on nonuniform discrete domains

• Published in: Journal of difference equations and applications Vol. 23; no. 5; pp. 878 - 892
• Main Authors: Belikov, J., Kaparin, V.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04-05-2017; Taylor & Francis Ltd
• Subjects: 34D20; Coefficients; Control stability; control system; Economic models; exponential stability; Linear control; Linear dynamic equation; Linear systems; time scales
• ISSN: 1023-6198; 1563-5120
• DOI: 10.1080/10236198.2017.1304931

The paper addresses the problem of exponential stability of linear control systems defined on nonuniform discrete domains. The main goal of this research is to find necessary and sufficient stability conditions in terms of the coefficients of the characteristic polynomial, associated with a system, and to study the geometry of stability regions, determined by the derived conditions in the coefficient space. As the first step in this direction, this paper presents such conditions for a special case of second-order systems defined on a discrete time scale with two asymptotic graininesses. The geometry of the corresponding regions in the coefficient space is illustrated for different values of the asymptotic graininesses.