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Technology scaling in sub-100 nm regime has significantly shrunk the SRAM stability margins in data retention, read and write operations. Conventional static noise margins (SNMs) are unable to capture nonlinear cell dynamics and become inappropriate for state-of-the-art SRAMs with shrinking access time and/or advanced dynamic read-write-assist circuits. Using the insights gained from rigorous nonlinear system theory, we define the much needed SRAM dynamic noise margins (DNMs). The newly defined DNMs not only capture key SRAM nonlinear dynamical characteristics but also provide valuable design insights. Furthermore, we show how system theory can be exploited to develop CAD algorithms that can analyze SRAM dynamic stability characteristics three orders of magnitude faster than a brute-force approach while maintaining SPICE-level accuracy. We also demonstrate a parametric dynamic stability analysis approach suitable for low-probability cell failures, leading to three orders of magnitude runtime speedup for yield analysis under high-sigma parameter variations.