Complete Robust Stability Domain of Fractional-Order Linear Time-Invariant Single Parameter-Dependent Systems With the Order 0 < α < 2

Abstract

The complete robust stability domain of fractional-order linear time-invariant single parameter-dependent systems with the system order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,2)$ </tex-math></inline-formula> is investigated in this brief. Firstly, the complete robust stability domain of such parameter-dependent systems is given using the Kronecker sum and the Bialternate sum respectively. The complexity of the algorithm can be reduced with Bialternate sum. This method can be easily extended to the case of multiple parameters. The final numerical examples are used to demonstrate the method proposed in this brief is effective and less conservative than the previous results.