State feedback stabilization of cascaded nonlinear systems with discontinuous connection

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