Qualitative features of matrix pencils and DAEs arising in circuit dynamics

摘要: The dynamical behaviour of nonlinear electrical circuits is usually modelled in the time domain by differential–algebraic equations (DAEs). formalism drives qualitative analyses based on linearization to a matrix pencil setting. In this context, present paper performs spectral analysis pencils and DAEs arising circuit theory. Specifically, non-singularity, hyperbolicity asymptotic stability equilibria are addressed terms topology. framework puts results beyond those already known for state-space models, unfeasible many actual problems. topological conditions study proved independent supporting index, therefore they apply both index-1 index-2 configurations. approach illustrates how graph theory, DAE theory interact circuits. ¶Preliminary research were present...