Signed-maximum minimization problem for SISO continuous-time systems

In this paper, we study the problem of minimizing signed (negative or positive) maximum amplitude of a regulated output, due to a fixed input. Like L_∞ (l_∞) problems, the optimal performance can be computed from dual formulation. However, from the lack of the alignment condition, the optimal solution can not be simply specified, if it exists. We also find suboptimal solutions to this problem and specify its form