A strict Lyapunov function for non-holonomic systems under persistently-exciting controllers

We study the stability of a non linear time-varying skew symmetric systems ẋ = A (t, x) x with particular structures that appear in the study problems of non holonomic systems in chained form as well as adaptive control systems. Roughly under the condition that each non diagonal element of A (t, x) is persistently exciting or uniform δ persistently exciting with respect x. Although some stability results are known in this area, our main contribution lies in the construction of Lyapunov functions that allows a computation of convergence rate estimates for the class of non linear systems under study.