Parameter-dependent LMI condition for stability analysis of fractional-order linear time-invariant single parameter-dependent systems

The robust stability problem of FO-LTI (fractional-order linear time-invariant) single parameter-dependent systems is studied in this paper with the system order 1 < γ < 2. A polynomial-type matrix which is limited with bounded, computable degree in the LMI condition is proposed using the Kronecker product and Kronecker sum and can be applied in sufficient and necessary conditions for the stability conditions for such single parameter-dependent systems. This condition can also help calculate the range of parameter when the system stays stable. An example is used to prove that the main theorem is valid and may be applied.