A general result on non-existence of finite-time stable equilibria in fractional-order systems |
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| Authors: | Aldo-Jonathan Muñoz-Vázquez Anand Sánchez-Orta Vicente Parra-Vega |
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| Institution: | 1. CONACYT – School of Engineering, Autonomous University of Chihuahua (UACH), Chihuahua, Mexico;2. Robotics and Advanced Manufacturing, Center for Research and Advanced Studies (CINVESTAV), Saltillo, Coahuila, Mexico |
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| Abstract: | 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. |
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| Keywords: | Corresponding author |
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