Finite-time stability of fractional-order nonlinear systems
Zaiyong Feng, Zhengrong Xiang
Abstract
The paper studies the finite-time stability (FTS) of equilibrium points (EPs) in fractional-order nonlinear systems (FONSs). Classifying the EPs into initial EP and finite-time EP innovatively, equations of the EPs in FONSs are investigated comprehensively, and a unified definition depicting the EPs in the FONSs is proposed. Furthermore, sufficient conditions of the FTS of EPs in FONSs are given. The proposed results are verified with an illustrative example. Thus, different from existing works that declare non-existence of finite-time stable equilibria in FONSs, the existence of finite-time stable EPs in FONSs is confirmed in this paper.
Topics & Concepts
Nonlinear systemStability (learning theory)MathematicsOrder (exchange)Applied mathematicsFractional-order systemControl theory (sociology)Fractional calculusComputer sciencePhysicsControl (management)Artificial intelligenceMachine learningQuantum mechanicsFinanceEconomicsFractional Differential Equations SolutionsAdvanced Control Systems DesignAdvanced Differential Equations and Dynamical Systems