Low-Order L1 Optimal Control Design via LMI

This paper develops a low-order l1 optimal controller design method for linear continuous time-invariant two-input, two-output systems. The new technique, which is proposed as an algorithm, combines the original concept of peak-to-peak gain of design system with optimal control theory and employs a free design parameter allowing for a flexible management of the tradeoff between robustness to disturbance signals and magnitude of the worst peak-to-peak gain of the design system. For solving this nonconvex problem, several linear construction and coprime factors so that based on strictly positive real function have been used.