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The first half of this manuscript deals with a review of different variants for second-order balanced truncation techniques for stable second-order form systems. Later, multiple nonexisting extensions of model order reduction techniques for stable and unstable second-order form systems are proposed. The framework for gramians based frequency or time (or both) limited model order reduction is presented. Comments on the preservation of large order system properties in the reduced-order model (ROM) that include structure and stability are discussed, and consequent conditions for the preservation of these properties in ROM are stated. The proposed techniques are tested on multiple benchmark/self-generated examples for successful validation of presented developments. The superiority of proposed extensions over existing techniques is also validated. The presented study can be utilized as a resource for infinite and finite interval model order reduction applications of continuous or discrete, stable, or unstable second-order form systems.

Infinite and Finite Time-Frequency Interval Based Variants of Second-Order Balanced Truncation for Stable and Unstable Systems