This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.
Alaviyan Shahri, E. S., Alfi, A., & Tenreiro Machado, J. A. (2015). An extension of estimation of domain of attraction for fractional order linear system subject to saturation control. Applied Mathematics Letters, 47, 26–34. https://doi.org/10.1016/j.aml.2015.02.020