New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a necessary and sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finitetime controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the system in finite time. Finally, we present simulation results for each of these cases, showing the efficacy of the designed control laws.