A new method to design discontinuous stabilizing controllers for chained systems

In this paper, we propose a new method to design discontinuous stabilizing controllers for chained systems. The proposed controllers yield exponential convergence of the states to the origin. In our method, the closed loop system of a chained system is formulated by a linear differential equation with a regular singular point at z = 0. It is shown that the controller design method proposed by Astolfi, in which σ process is used for a coordinate transformation, is included in our method as a special case where the linear differential equation with a regular singular point at z = 0 is limited to its subclass, namely an Euler differential equation. This method can be easily extended to apply to multiple chained systems. The simulation results demonstrate the effectiveness of our method.