An efficient algorithm for frequency-weighted balanced truncation of VLSI interconnects in descriptor form

TLDR: An efficient frequency-weighted balanced truncation algorithm without finding the spectral projectors is proposed that is accurate and efficient and used to ensure passivity of RLC interconnect models.

Abstract: Balanced truncation of descriptor systems requires computation of spectral projectors and solution of the generalized projected Lyapunov equations, both of which have significant complexity. Frequency-weighted balancing methods are more efficient if the response over a specific frequency range is desired. However, a direct extension of these methods to descriptor systems requires the spectral projectors. In this paper, we propose an efficient frequency-weighted balanced truncation algorithm without finding the spectral projectors. Samples of the frequency-domain solution to the system are used to get an accurate estimate of the improper Gramians. The proper Gramians are computed after adjusting for the contribution of the improper subsystem. Low rank factors of these Gramians are used to obtain a basis that includes the contribution of both the proper and improper subsystems. Congruence transform is used to ensure passivity of RLC interconnect models. Results for standard benchmarks show that the method is accurate and efficient.