This paper explains how to stabilize a "nonholonomic integrator" using a hy
brid control law employing switching and logic. Results concerning asymptot
ic stability and exponential convergence to the origin are derived. The not
ion of a (positively) invariant set is extended to hybrid systems and suffi
cient conditions for invariance are presented. The verification of these co
nditions does not require the computation of the state trajectories and the
ir use goes beyond the analysis of the system presented in this paper. (C)
1999 Elsevier Science Ltd. All rights reserved.