Model reduction by moment matching for linear singular systems

Abstract

Abstract-The paper presents a moment matching approach to the model reduction problem for singular systems. Combining the interpolation-based and the steady-state-based description of moment, a partitioned formulation of the Krylov projector is obtained. Several implications of this result are investigated and different families of reduced order models are proposed. The possibility to maintain structural properties of the fast subsystem is studied. Two examples illustrate the results of the paper.

A note on the electrical equivalent of the moment theory

“…Moreover, the equivalence that we have established between moments and phasors lends itself to the extension of the phasor transform beyond the discontinuous linear framework. In fact, the moment theory has been extended to nonlinear systems [4], time-delay systems [7] and differential-algebraic systems [20]. New generalizations of the phasor analysis could be achieved exploiting the equivalence pointed out in this note.…”

Steady-State Matching and Model Reduction for Systems of Differential–Algebraic Equations

“…The eigenvalues of the dynamic matrix of the model (29) have been set, using the free parameter G, as −0.1021, −4.8979. These eigenvalues are the eigenvalues of the linearization around u C1 = 0, Φ = 0 of system (28). Similarly, the only finite eigenvalue of model (30) is set as −0.1021.…”

“…Preliminary versions of this technical note have been published in [28] and [29]. The additional contributions of the technical note are as follows: we provide all the proofs of the results (in the Appendix); the presentation has been improved, developing the results for nonlinear systems and then deriving the linear framework as a special case; we study the controllability and observability properties of the linear reduced order models; we illustrate the results with two examples, namely we compute the moment in an academic example and we obtain reduced order models for a nonlinear system describing an electrical circuit.…”

Constrained optimal reduced-order models from input/output data

“…If the interest of the designer is to have the best approximation along all the frequencies, then the unconstrained problem should be used. On the other hand if the designer knows that the system is driven by a specific class of input signals (as it is desirable when moment matching is preferred with respect to other reduction methods), for instance like in the case of the reduction of power systems [36], [42], then the constrained problem should be solved.…”