Analysis of fractional-order linear systems with saturation using Lyapunov’s second method and convex optimization

Abstract

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.