Yang, Y., Wu, J., Xiong, R., Xu, W. and Chen, Sheng
Single-input and single-output (SISO) controller reduction based on the $L_1$-norm
Asia-Pacific Journal of Chemical Engineering, 3, (6), .
This paper proposes a new method to solve the controller-reduction problem based on the $L_1$-norm. This method uses a reduced-order closed-loop system to deduce reduced-order controllers. The problem of obtaining the required lower-order closed-loop system was formulated as an $L_1$-norm optimization, and the conditions were provided for guaranteeing the internal stability and the existence of lower-order controllers from the obtained reduced-order closed-loop system. In addition, the particle swarm optimization and sequence linear programming were adopted to solve the resultant $L_1$-norm optimization. Two numerical examples demonstrated the effectiveness of the proposed method.
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