Comments on "Adaptive control of linearizable systems" by S.S. Sastry and A. Isidori

In the above-titled paper by S.S. Sastry and A. Isidori (ibid., vol.34, p.1123-31, Nov. 1989), the use of feedback linearizing controls for adaptive control of nonlinear systems which have an unknown linear parameterization is discussed. The requirement that a nonlinear system of relative degree greater than one be globally Lipschitz continuous is quite strong. The commenters argue that the theorems of Sastry and Isidori fail when that hypothesis is relaxed by providing simple examples of systems which cannot be globally stabilized with their proposed adaptive feedback linearizing control law.<>