A general result on non-existence of finite-time stable equilibria in fractional-order systems

It is well known that a fractional-order system with a continuous right hand side does not have finite-time stable equilibria, but the discontinuous case has remained elusive in literature. Thus, based on novel mathematical tools, recently published in literature, it is demonstrated that attaining finite-time stable equilibria is not possible for a fractional-order system, not even in the case of an impulsive or discontinuous feedback. In consequence, it is demonstrated that, for a fractional-order system, a Lyapunov stable equilibrium cannot be at the same time finite-time stable.