Finite-time stability of cascaded time-varying systems

The uniform global finite-time stability is discussed for a cascaded time-varying system consisting of two uniformly finite-time stable subsystems. It is shown that a forward completeness condition is enough to ensure the uniform global finite-time stability of the system. For ease of reference, a particular result with a growth rate condition is also deduced. These stability results are applied to the tracking control problem of a non-holonomic wheeled mobile robot in kinematic model. Two tracking control laws are developed respectively for two different cases of the desired rotate velocity. Both control laws are continuous and can control the mobile robot to track the desired trajectory in finite time. Simulation results are provided to show the effectiveness of the method.