Esmat Sadat Alaviyan Shahri and Saeed Balochian. Analysis of Fractional-order Linear Systems with Saturation Using Lyapunov s Second Method and Convex Optimization. International Journal of Automation and Computing, vol. 12, no. 4, pp. 440-447, 2015. https://doi.org/10.1007/s11633-014-0856-8
Citation: Esmat Sadat Alaviyan Shahri and Saeed Balochian. Analysis of Fractional-order Linear Systems with Saturation Using Lyapunov s Second Method and Convex Optimization. International Journal of Automation and Computing, vol. 12, no. 4, pp. 440-447, 2015. https://doi.org/10.1007/s11633-014-0856-8

Analysis of Fractional-order Linear Systems with Saturation Using Lyapunov s Second Method and Convex Optimization

doi: 10.1007/s11633-014-0856-8
  • Received Date: 2013-09-05
  • Rev Recd Date: 2014-04-02
  • Publish Date: 2015-08-01
  • In this paper, local stability and performance analysis of fractional-order linear systems with saturating elements are shown, which lead to less conservative information and data on the region of stability and the disturbance rejection. Then, a standard performance analysis and global stability by using Lyapunov s second method are addressed, and the introduction of Lyapunov s function candidate whose sub-level set provide stability region and performance with a restricted state space origin is also addressed. The results include both single and multiple saturation elements and can be extended to fractional-order linear systems with any nonlinear elements and nonlinear noise that satisfy Lipschitz condition. A noticeable application of these techniques is analysis of control fractional-order linear systems with saturation control inputs.

     

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