Combined balanced truncation algorithm and linear differential mapping for controller order reduction problem

Model reduction is a problem that has been obtaining more attention in recent years. One of the most commonly used algorithms in model order reduction is the balanced truncation algorithm. Based on the balancing algorithm, many algorithms have been proposed. The paper proposes a combined balanced truncation algorithm and linear differential mapping for the order reduction problem of stable linear systems. Besides, the authors also applied the proposed method to reduce the order of robust high-order controllers in two-wheeled self-balancing vehicles. The simulation results will illustrate the response of the control system when using the reduced-order controller utterly similar to the response of the control system using the original controller.