An algorithm for the H∞ control of switched linear systems via Hamilton-Jacobi-Isaacs formulation

This paper proposes a novel approach to address the H∞ control problem of switched linear systems through the assignment of the switching law. Exploiting the relationship existing between H∞ control problems and differential games, which has been analyzed in depth in the literature, we reformulate the original control problem as the solution of a Hamilton-Jacobi-Isaacs equation depending on the switching signal. The solution of such an equation is not trivial in general, but an effective numerical procedure is proposed to deal with it in the case of planar systems.