Guaranteed stable projection-based model reduction for indefinite and unstable linear systems

In this work we present a stability-preserving projection framework for model reduction of linear systems. Specifically, given one projection matrix (e.g. a right-projection matrix), we derive a set of linear constraints for the other projection matrix (e.g. the left-projection matrix) resulting in a projection framework that is guaranteed to generate a stable reduced model. Several efficient techniques for solving the proposed system of constraints are presented, including an optimization problem formulation for finding the optimal stabilizing projection, and a formulation with computational complexity independent of the size of the original system. The resulting algorithms can create accurate stable and passive models of arbitrary indefinite systems at a significantly cheaper cost than existing methods such as balanced truncation. Nevertheless, our algorithms integrate fully and effortlessly with most of the available standard model order reduction approaches for very large systems generated in VLSI applications (such as moment-matching methods, POD, or Poor Man's TBR), which can guarantee stability and passivity only in very specialized cases. Our algorithms have been tested on a large variety of typical VLSI applications, including field-solver-extracted models of RF inductors for analog applications, power distribution grids for large VLSI digital integrated circuits, and MEMS devices for sensing and actuation applications. The results have been successfully compared to those from existing and much more expensive stabilizing reduction techniques.