Homogeneous constrained finite-time controller for double integrator systems : analysis and experiment

In this paper, the finite-time control problem for a class of double integrator systems under state constraints is investigated. Different from the traditional finite-time control methods with constant gains, an improved finite-time controller with state-dependent gains is designed. The main challenges lie in the finite-time stability analysis of the resultant closed-loop system caused by state-dependent control gains and how to make the system states keep in the constrained region. Based on the homogeneous system theory, the finite-time stability of the closed-loop system under state constraints is proved. In addition to the finite-time convergence, it is also shown that the states of the system always are kept in the constrained region. Finally, the developed finite-time controller is applied to buck converter and the validity of the proposed method is verified through a DC-DC buck converter under voltage and current constraints.