Computation of spectral sets for uncertain linear fractional-order systems

The present paper proposes an algorithm to compute the spectral set of a family of fractional-order pseudo-polynomials. The algorithm makes use of interval constraint propagation technique to find out all the structural roots of the given uncertain fractional-order systems in the given search domain. It is first shown that the problem of finding the spectral set can be formulated as an interval constraint satisfaction problem and then solved using branch and prune algorithm. The algorithm guarantees that all the points of the spectral set are computed to prescribed accuracy. The proposed algorithm is demonstrated on a plant with nonlinear parametric dependencies and also on a practical application of a gas turbine plant.