Quantitative design for multivariable systems with uncertainty

In this paper we propose a robust controller design method of uncertain multivariable systems. Two decoupling methods are first derived such that an n-dimensional uncertain multiple-input multiple-output system can be almost decoupled into n single-input single-output (SISO) subsystems, where the controlled plant with worst-case interactions between inputs and outputs is considered for decoupler design. Once the diagonal dominance is reached, the well-established SISO quantitative feedback theory technique can then be employed to design individual robust controller for each channel of the almost decoupled plant such that the required performances are achieved. A numerical example is given to illustrate the feasibility of proposed methods.