On checking dissipativity of parameterized linear and time-invariant circuits and systems

A novel dissipativity characterization is proposed for linear time-invariant circuits and systems whose dynamic behavior depends on one external parameter. The proposed formulation extends to the parameterized case standard Hamiltonian-based algebraic dissipativity characterizations and is structured as an underdetermined multiparameter eigenvalue problem. Resulting from a polynomial parameterization, the proposed characterization leads to an effective set of algorithms that are able to determine the regions of local dissipativity and local activity in the frequency-parameter plane, which in turn can be exploited by dissipativity enforcement algorithms to produce uniformly passive models. The reference application of proposed technique is behavioral modeling of complex circuits or systems, whose dynamic behavior can be compressed into a low-order system through dedicated model order-reduction processes. Various examples ranging from integrated components to microstrip filters and networks are used to illustrate the proposed characterization.