Quantitative design method for MIMO uncertain plants to achieve prescribed diagonal dominant closed-loop minimum-phase tolerances

A quantitative design method for multi-input multi-output linear time-invariant feedback systems for plants with large uncertainty has been presented by Horowitz ( 1982), and by Yaniv and Horowitz ( 1986). This design method is developed here to guarantee minimum-phase closed-loop diagonal elements for systems with basically non-interacting (Horowitz and Loecher 1981) off-diagonal closed-loop tolerances. The advantage of this design is that with minimum-phase transfer functions, a very important class of time-domain specifications can be translated to the frequency domain, as shown by Krishman and Cruickshanks ( 1977) and by Horowitz ( 1976). The attractive properties of this design method are: (a) the problem is reduced to a successive single-loop design with no interaction between the loops, and no iterations are necessary; (b) the technique can be applied to all n × n plants P with P −1 having no poles in the right-half plane, and satisfying some conditions described in § 5; (c) the procedure is interactive with n steps for an n × n MIMO plant, and in each step, one of the elements of the diagonal feedback compensation and one row of the prefilter matrix are designed.