LMI Tools for Stability Analysis of Fractional Systems

Abstract

The main point when dealing with Linear Matrix Inequalities (LMI) is convexity. However, with state space representation of fractional systems, the stability domain for a fractional order 0 < ν < 1 is not convex. The classical stability condition thus cannot be extended to fractional systems. In this paper, three LMI based methods are used to characterize stability. The first is based on the second Lyapunov method and provides a sufficient but non-necessary condition. The second and new method provides a sufficient and necessary condition, and is based on a geometric analysis of a fractional system stability domain. The third method is more conventional but involves non strict LMI. A comparison of the first two methods is provided.