THE STABILITY PROPERTIES OF LINEAR DESCRIPTOR DIFFERENTIAL SYSTEMS WITH ADDITIONAL DISTURBANCES

摘要

In this paper, two very basic concepts of stability for linear descriptor differential systems with consistent initial conditions and additional regular disturbances are being considered. These kinds of systems are appeared in many modelling processes; see for instance the literature of power systems, electrical circuits, growth population phenomena (Leslie model), even some financial and actuarial claims processes etc. Using the well-known complex Weierstrass canonical form of the associated matrix pencil, the state equation is decomposed into two subsystems, whose solutions are being provided. Moreover, the assumption of the consistency of the solution provides us with both stability and asymptotic stability, which in practice are depended on the real part of the finite elementary divisors.