Quantitative design of uncertain multivariable control system with an inner-feedback loop

An additional inner-feedback loop is used to reduce the channel interaction of a multivariable control system such that the design of the outer-feedback loop can be treated as a single-variable problem for ease in achieving the required main-channel performance. The relative error between the exact input-output relation t_ii(jω) of channel i and its approximation tˆ_ii(jω)={l_i(jω)f_ii (jω)}/{1+l_i(jω)} is introduced to provide an effective measure for assessing the achieved noninteraction. According to the approach proposed, the single-input/single-output quantitative-feedback-theory design method can be applied directly for the design of both inner- and outer-feedback loops