A schematic study of dimension reduction techniques for complex high-order integer, fractional and interval systems

The field of model order reduction (MOR) has seen significant advancements in addressing the challenges associated with the complexity of mathematical models in engineering and physical sciences. This paper provides a schematic study of MOR techniques applicable to linear time-invariant integer order, fractional order and interval systems. Various classical and optimization methods are elaborated highlighting their effectiveness in reducing system dimension and maintaining the essential dynamic characteristics. Emphasis is given to the distinct approaches required for integer, fractional and interval systems, given their unique mathematical properties and application-specific challenges. The optimization techniques integral to the reduction process are schematically investigated, focusing on balancing accuracy, computational efficiency and stability in the reduced models. Through a detailed comparison of these methods, the advantages and challenges of each approach are presented, providing critical insights into their suitability for different classes of systems. Although classical techniques have been extensively employed independently and combined with soft computing techniques for integer-order systems, lesser emphasis is paid to fractional-order and interval-system’s order reduction. Several issues such as unstable systems, steady-state errors, passivity and non-minimum phase characteristics still pertain and not addressed simultaneously in existing techniques. The lack of generality of the methods proposed in literature further motivates researchers to work on this years old problem. This review serves as a valuable resource for researchers seeking to understand the state of the art in MOR methods and their applications, offering guidance on selecting appropriate techniques based on system characteristics and reduction objectives. The analysis concludes with suggestions for future research directions aimed at enhancing the robustness and applicability of MOR techniques across various domains.