Single-input and single-output (SISO) controller reduction based on the L1-norm

This paper proposes a new method to solve the controller-reduction problem based on the L1-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 L1-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 L1-norm optimization. Two numerical examples demonstrated the effectiveness of the proposed method.  2008 Curtin University of Technology and John Wiley & Sons, Ltd.