Sign-weighted peak minimization problem for feedback systems

This note studies the problem of minimizing a parameterized convex combination of the overshoot and undershoot of a single-input-single-output (SISO) discrete-time system to a fixed input. We provide a simple condition for the solution existence and characterize the structure of optimal solutions. It is shown that a known l_∞ suboptimal scheme also works in our problem. In addition, we make a comparative analysis with the l_∞ problem