On the time-domain performance of multivariable systems in response to fixed inputs

The synthesis of compensators for tracking applications in LTI discrete-time systems is investigated from the time-domain perspective. The problem of simultaneously minimizing the 'size' of the error and control-input signals to specific reference inputs is considered. The control problem is expressed in a linear programming framework, in which the weighted sum of l1-norms of the error and control-inputs in each channel is minimized, subject to time-domain constraints. The Youla parametrization is used to obtain the feasible set of all admissible error and control-input pairs from which a stabilizing compensator can be synthesized. The flexibility of the method is illustrated by application to novel types of timedomain constraints, and demonstrated by the use of a numerical example.