On the $$\mu $$μ -Analysis and Synthesis of MIMO Lurie-Type Systems with Application in Complex Networks

The main contribution of this paper is to present a new approach to the analysis of the absolute stability of multiple-input–multiple-output (MIMO) Lurie-type systems using $$\mu $$-analysis and linear fractional transformations from the robust control theory. As a consequence, and also as an important contribution, the technique proposed enables the design of controllers via DK-Iteration for Lurie-type systems. For these, one extends the results obtained for Lurie-type systems to a closed-loop version of it. In addition, it is also conjectured that it is possible to make use of this new approach in time-delay MIMO Lurie-type systems. The obtained results allow a generalization of the theory for the analysis and design of controllers that can be useful in complex networks. Examples and comparisons with other results are given to illustrate the effectiveness of the methods of this paper.