Abstract
In this paper, we deal with the control problem of a class of non-holonomic systems with m input variables. In the system, if the input vector fields and the first level of Lie brackets between them span the tangent space at each configuration, the system can move in every direction using the first level of Lie bracket motions and it is controllable. This class of systems is called as first order systems. We derive a time-invariant discontinuous state feedback law for the system based on the Lyapunov control: The input is designed so that the derivative of the Lyapunov function is composed of a symmetric and an asymmetric bilinear form in the gradient vectors of the Lyapunov function. In the controlled system, the desired point is the only stable equilibrium point. The performance of the controller is verified by numerical simulations.
