An LMI approach to peak-to-peak gain minimisation: filtering and control

The authors take a new approach to the problem of peak-to-peak gain minimization (the L₁ or induced L_∞ problem) Instead of minimizing the induced L_∞ norm, they minimize the *-norm, an upper bound on the induced L_∞ norm. The filters and controllers that result are of low order (same as the plant), and synthesis reduces to minimizing a real function of a real variable. This function can be efficiently evaluated by solving a linear matrix inequality (LMI) eigenvalue problem, but the problem of minimizing this function has not yet been satisfactorily resolved. Only strictly proper filters and controllers are considered here.