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

Abstract

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.

Keywords:

• Linear dynamic equation
• control system
• exponential stability
• time scales

AMS Subject Classifications:

• 34D20
• 34N05
• 93C05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of V. Kaparin was supported by the Estonian Research Council, personal research funding [grant number PUT481].