Quantitative robust diagonal controller design for Mimo systems

In this paper we present a robust decoupled controller design method for MIMO systems by combining Perron-Frobenius (PF) theory, Ostrowski's theorem and quantitative feedback theory (QFT). Our aim is to find a required robust controller with less complexity, namely to keep the number of ‘cross-couplings’ of the controller as low as possible. To this end, the PF theory is first adopted to almost decouple the n-dimensional perturbed MIMO inverse system into n SISO inverse subsystems, where the synthesized decoupler has a diagonal form. Moreover, Ostrowski's theorem allows us to design a constant feedback gain matrix with diagonal form such that the compensated inverse plant is of more diagonal dominance. The SISO QFT technique is then utilized to design a robust diagonal controller for each single loop of compensated plant. Ultimately, the required robust stability and tracking performance can indeed be achieved by the designed robust decoupled controller. Two numerical examples are given to illustrate that not only are all the required performances achieved, but also that the combined technique for designing a robust decoupled controller for a perturbed MIMO system is actually workable.