Decomposition of Descriptor Control Systems

We establish the conditions to decompose a complex descriptor control system into simpler subsystems. The system state and input are described by equations not solved with respect to the derivative of the state. We consider two types of decompositions: sequential and parallel ones. The decomposition conditions are formulated in terms of the existence of invariant pairs of subspaces for operator pencils consisting of system coefficients. The results are illustrated by the example of a descriptor system that describes transient states in a radio-engineering filter. We perform the cascade–parallel decomposition of forth-order filter into the simplest first-order filters, each containing one inertial element.