New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers
It provides a novel method for finite-time stabilization of linear systems, which is important for control theory applications requiring precise settling times.
The paper develops new controllers achieving finite-time stability for linear systems, using geometric conditions and barrier functions, with simulations validating the approach.
This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time 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.