Circuits, Systems, and Signal Processing https://doi.org/10.1007/s00034-018-0912-7 Order Reduction in z -Domain for Interval System Using an Arithmetic Operator Amit Kumar Choudhary 1,2 · Shyam Krishna Nagar 1 Received: 7 October 2017 / Revised: 25 July 2018 / Accepted: 27 July 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper deals with order reduction in discrete-time systems. The reduction tech- nique is based on utilization of Routh approximation and multiplicative operator. Various combinations of Routh table are used to derive the desired numerator and denominator polynomial of reduced-order model. Numerical examples are presented to verify the proposed algorithm. Keywords z-Domain interval systems · Order reduction · Multiplicative operator · Routh approximation 1 Introduction Modelling of a physical system and its controller design often result in higher-order mathematical representation. The analysis of such higher-order systems is tedious and complicated demanding an appropriate model order reduction technique. The available methodologies for model reduction in non-interval systems offer well-known algorithm: Routh approximation (RA). The approximation features the advantage of simplicity in mathematical computation and stability retention of the resulting reduced model. Due to the above-mentioned advantages, the researchers have focused their attention on possible extension to other type of systems. The continuous- time RA is applied to discrete-time systems by using an appropriate transformation. Further, the attention of the researchers was drawn to extend the method to interval B Amit Kumar Choudhary amit.rs.eee@iitbhu.ac.in Shyam Krishna Nagar sknagar.eee@itbhu.ac.in 1 Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University) Varanasi, Varanasi, U.P. 221005, India 2 Present Address: Department of Electrical Engineering, BIT Sindri, Dhanbad, Jharkhand 828123, India