On Stability of Descriptor Fractional Linear Control Systems with Regular Pencils

Abstract

This paper presents novel stability results for descriptor fractional proportional linear control systems governed by generalized Caputo derivatives. Classical stability notions are extended to fractional settings by introducing Mittag–Leffler stability and asymptotic stability conditions. The analysis distinguishes between nonsingular and singular cases of the system matrix F. In the nonsingular case, explicit solutions are obtained via the generalized Laplace transform, while in the singular case, under regularity of the matrix pencil, a decomposition method is applied. Stability criteria are expressed in terms of eigenvalues of the system matrix G, fractional parameters θ and ρ, and the placement of poles in the complex plane. Examples illustrate the theoretical results, providing a rigorous framework for fractional-order control system analysis.