s can be extended to handle periodically time-varying ones as well. In [Moll00] this representation was adopted to analyze the stability of power supply networks. However, although the treatments in [Were91a, Moll00] overcome many of the shortcomings in [Maas88], dealing with the o-dimensional nature of the matrix is still inefficient. Also, little attention is given to the structural properties that characterize the matrix representation. 3.2.4 Contributions of this work Finally, although not always mentioned explicitly, this matrix formulation also under- lies many other approaches for frequency-domain analysis of LPTV system behavior [Phil98, Royc98, Royc99, Teli96]. As most of these methods target numerical analy- sis, they deal with the matrix inversions through truncation and Krylov subspace tech- niques. 3.2.4 Contributions of this work This chapter adopts the HTM framework for Laplace-domain (frequency-domain) analy- sis of LPTV system behavior. It contributes to the theory on HTMs in the following ways: As far as theory is concerned, results previously scattered over different publi- cations and application areas [Maas88, Molloo, Royc98, Were91a] are collected in a coherent framework. To the author's knowledge, this treatment is the first of its kind in elaborating the HTM framework in its full strength. Existing results are made consistent with each other. Additionally, the way in which results are derived and synthesized is original. The derivations emphasize clear-cut physi- cal interpretations while avoiding too high a degree of mathematical abstraction. Moreover, they lend themselves to extend the HTM concept towards arbitrary classes of (non-periodic) LTV systems. Even more than prior treatments, emphasis is placed on making it practical to apply the HTM framework. We develop methods for approximate computa- tions that render HTM-based analysis of many practical systems and circuits better feasible. It is shown how complex operations, like the inversion of 8- dimensional HTMs needed to solve feedba