Quadratic repulsiveness for LTI systems: Definition, analysis and design

This paper introduces and describes the notion of quadratic repulsiveness for linear time-invariant systems. Such novel concept arises from the goal of escaping from an undesirable region of the state space represented by the super level sets of an indefinite quadratic function. The analysis of the special eigenstructure of a system attaining quadratic repulsiveness is carried out first, revealing a number of interesting properties. Design algorithms based on LMIs are proposed for the synthesis of controllers enabling for the simultaneous stabilization and repulsiveness of the closed-loop system. The theoretical results in this paper are illustrated through examples that show the main features of quadratic repulsiveness.