Analysis and synthesis of single-input-single-output Lurie type systems via H ∞ mixed-sensitivity

Abstract

The goal of this paper is to present a different approach to the analysis of the absolute stability of Lurie type systems in the single-input-single-output (SISO) case using robust control theory. The proposed technique enables the design of controllers via ${\mathcal{H}}_{\infty }$ mixed-sensitivity (S/KS/T), where, besides making the system absolutely stable, the performance problem can also be solved. In addition, it is also demonstrated that it is possible to make use of this new approach in time-delay Lurie type systems. Thus, through a new methodology, this work paves the way to the study of the absolute stability of multiple-inputs-multiple-outputs (MIMO) systems, aiming at a better generalization of the theory and enabling applications in other areas, such as neural networks. Examples, numerical simulations and application in Chua’s circuit are given to illustrate the results.