Floquet Theory and Stability

Abstract

In this chapter, the free-input periodic system x(t +1) = A(t)x(t) (3.1) is considered, with A(t) of constant dimension n×n. First, the properties of the monodromy matrix are pointed out. This opens the way to the celebrated Floquet theory, which deals with the problem of finding a periodic state–space transformation, so that, in the new basis, the dynamic matrix is constant. The issue of periodic system stability follows, together with the notion of periodic Lyapunov function and periodic Lyapunov inequality. Finally, the concept of quadratic stability is introduced as a tool for the stability analysis of periodic systems subject to parameter uncertainty.