Finite-Time Stabilization for Continuous Triangular Systems via Vector Lyapunov Function Approach

This article provides finite-time stabilizing control laws for the continuous triangular systems, in which the nominal dynamics is the chain of power integrators with the power of a positive odd rational number. For a class of continuous lower-triangular systems, the linear controllers are designed. By invoking a vector Lyapunov function theory, there is no need to use the usual back-stepping technique and a quite number of inequality computations are avoided. For a class of continuous upper-triangular systems, the nested-saturation controllers are constructed. In this case, the use of a vector Lyapunov function theory also helps to reduce computational burden, and allows us to summarize a same group of parameter conditions guaranteeing both the reduction of saturated terms and the finite-time stability of the reduced system.