Continuous Control Designs for Stabilizing Chained Systems; A Global State Scaling Transformation and A Time Scaling Method

In this paper, two methods are proposed to recover uniform complete controllability for the chained system. One involves a global singularity-free state scaling transformation, the other is based on a time transform, and both of them require an innovative design of dynamic control component u₁. Using either of the approaches, the chained system is mapped into a controllable linear time-varying system for which control can systematically be designed to ensure exponential convergence or asymptotic stability as well as optimal performance. Simulation results are used to verify the effectiveness of the proposed controls