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Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 509--524 | DOI:10.5890/DNC.2026.12.003

D. Naga Purnima$^1$, G.V.S.R. Deekshitulu$^2$, G.V. Ramana$^1$, M. Bala Prabhakar$^1$

$^1$ Department of Mathematics, Aditya University, Surampalem-533437, A. P., India

$^2$ Department of Mathematics, JNTUK Kakinada, Kakinada-533003, A.P., India

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Abstract

This paper presents a new framework for analyzing the stability of fractional-order digital control systems (FODCS) utilizing the N-transform method. In contrast to conventional techniques that rely on Laplace or Grunwald–Letnikov formulations, the proposed approach supports discrete-time modeling and allows for the visualization of stability regions through Riemann surface decomposition. The method derives closed-form unit step responses and introduces generalized stability criteria applicable to both linear and nonlinear systems. A comparative analysis with existing methods demonstrates improved interpret ability and computational efficiency, making this approach a valuable asset for advanced digital control applications.

Acknowledgments

The authors thank their respective college managements for their continuous support and constant encouragement. The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

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