Stability and Stabilization for Delay Delta Fractional Order Systems: An LMI Approach

The well-known delta fractional calculus is widely used in system analysis and synthesis. However, the irregular stable region brings many unexpected difficulties and challenges. The simple linear matrix inequality (LMI) condition, especially
$\alpha \in (1,2)$
, is lacking. This brief constructs a circular region to approximate the true stable region. Afterwards, the sufficient conditions in terms of LMIs are derived. It is shown that the elaborated results are valid and effective.