A new guardian map and boundary theorems applied to the stabilization of initialized fractional control systems

In the present work, some generalizations of the boundary crossing theorem and the zero exclusion principle are given for fractional order initialized systems. A new guardian map for the maximal stability interval is proposed as well as its relation with the boundary theorems is established. An extension of the technique for linear time invariant fractional order initialized systems to determinate the maximal stability interval is derived from the guardian map defined as a monoparametric pseudo-polynomials family. This technique is essentially the task of locating the zeros of the family of characteristic pseudo-polynomials of a linear fractional order system inside the stability region. Finally, an illustrative example is also provided to show the technique.