ityl or positive realness in a VLSI model is an important property Passivity in a VLSI model is an important property to guarantee sta-to guarantee stable global simulation [3,7]. Existing DS passivity ble global simulation. Most VLSI models are naturally described tests are restrnctive in different aspects. For example, the extended as descriptor systems (DSs) or singular state spaces. Passivity tests linear matrix inequality (LMI) test in [7] has a high complexity for DSs, however, are much

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... ss developed compared to their non-of 0(n5) to 0(n6), rendering it prohibitive in testing passivity of singular state space counterparts. For large-scale DSs, the existing high-order DSs, as is usual for VLSI models. The generalized al-test based on linear matrix inequality (LMI) is computationally pro-gebraic Riccati equation (GARE) test [8] works only in the limited hibitive. Other system decoupling techniques involve complicated case of admissible (regular, stable and impulse-free) DSs. coding and sometimes ill-conditioned transformations. This paper The contribution of this paper is the formulation of a fast 0(n3) proposes a simple DS passivity test based on the key insight that algorithm for checking passivity of a DS. The key insight is that the sum of a passive system and its adjoint must be impulse-free. when a (possibly impulsive) passive system is added to its adjoint, A sidetrack shows that the proper (non-impulsive) part of a pas-the resulting system, which is again a DS, must be impulse-free. sive DS can be easily decoupled along the test flow. Numerical Numerically efficient and reliable techniques in transforming skew-examples confirm the effectiveness of the proposed DS passivity Hamiltonian/Hamiltonian (SHH) matrix pencils are employed. Af-test over conventional approaches. ter removal of uncontrollable and unobservable impulsive modes, if any, passivity can then be checked through the positive semidefi-nite of the residue matrix and the proper part of the DS using stan-Categories and Subject Descriptors dard techniques (e.g., [9, 10]). Along the proposed test, numeri-1.6.5 [Simulation and Modeling]: Model Development-model-cally well-conditioned orthogonal transformations are used when-ing methodologies; J.6 [Computer-Aided Engineering]:-omputer-ever possible. The proper part of the original DS is also conve-aided design (CAD) niently decoupled as a sidetrack. Section 2 of this paper reviews the problem settings and important DS properties. Linear system transformations necessary for the General Terms development of the proposed test are covered. Section 3 presents Algorithms a walkthrough of the proposed DS passivity test under the framework of SHH matrix pencil transformations. Numerical results in Section 4 show the effectiveness of the proposed approach over