Minimization of the maximum peak-to-peak gain with time domain constraints on fixed input response

This paper studies the minimization of the l₁ norm of a closed loop map with time domain constraints of the transient response for a fixed input. A computational method to reduce the problem to finite dimensional linear programs is proposed. The framework uses the DA method which existed for the l₁ control without time constraints. Additional advantages such as no use of rank interpolation condition and no assumptions on FIR feasible solution are inherited to the time domain constraints version. An example is included to compare the proposed method and FMV method in the literature to show that order inflation can be avoided