Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems Academic Article uri icon

abstract

  • Based on proximal subdifferentials and subgradients, and instrumented with an extended Caputo differintegral operator, the stability analysis of a general class of fractional-order nonlinear systems is considered by means of non-smooth but convex Lyapunov functions. This facilitates concluding the Mittag–Leffler stability for fractional-order systems whose solutions are not necessarily differentiable in any integer-order sense. As a solution to the problem of robust command of fractional-order systems subject to unknown but Lebesgue-measurable and bounded disturbances, a unit-vector-like integral sliding mode controller is proposed. Numerical simulations are conducted to highlight the reliability of the proposed method in the analysis and design of fractional-order systems closed by non-smooth robust controllers.

author list (cited authors)

  • Muñoz-Vázquez, A., Parra-Vega, V., & Sánchez-Orta, A.

citation count

  • 5

publication date

  • April 2019