Prescribed-Time Control With Linear Decay for Nonlinear Systems

In this letter, a new notion of stability is introduced, which called triangular stability. A system triangularly stable if the norm its state vector bounded by decreasing linear function time such that intersection point with axis can be arbitrarily commanded user. Triangular implies prescribed-time stability, means nonlinear converged to zero equilibrium at an arbitrary finite time. controller guaranteed developed for normal form systems uncertain input gain, able reject disturbances and unmodeled dynamics. Numerical simulations are carried out visualize results second fourth-order systems.