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