Control design for systems in chained form with bounded inputs

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not Lipschitz continuous at the origin and hence they may use significant amount of control effort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing bounded convergent controllers (with exponential convergence rates) for nonholonomic systems in chained form