State Feedback Stabilization of Cascaded Nonlinear Systems with Discontinuous Connection

In the practical engineering, many natures are described as a discontinuous function of state variable, and the discontinuity is usually main reason that damages the control performance. For example, in the set-point control problem of mechanical system, the static friction which is described by a sign function of velocity of the contacting faces causes undesired positioning error. In this paper, we investigate the stabilization problem for a class of nonlinear systems that consist of two subsystems with cascaded connection. We show the basic idea with a special case first, and then the result was extended to more general cases. Some interesting numerical examples were given to demonstrate the effectiveness of the proposed design approach.