Robust l1 synthesis with error quantification for coprime factor nominal system

A priori information for optimal robust synthesis includesa nominal system and sets of perturbations and disturbances.This paper addresses the problem of optimal robust synthesisin the l1 setup when the nominal system is givenbut upper bounds for norm-bounded perturbations and exogenous disturbance are not known to controllerdesigner. We consider coprime factor nominal systems andshow that the worst-case norm of the system output isa linear fractional function of the induced norms of systemtransfer functions and the norms of perturbations anddisturbance. Iterative alternate optimization of this functionover the Youla parameters and the norms of perturbationsand disturbance that are not falsified by datais used for synthesis of robust controller.Efficiency of the method is illustrated by simulations.