Balancing and model reduction for second-order form linear systems

Model reduction of second-order form linear systems is considered where a second-order form reduced model is desired, The focus is on reduction methods that employ or mimic Moore's balance and truncate. First, we examine second-order form model reduction by conversion to first-order form and obtain a complete solutiopgn for this problem, Then, new Gramians and input/output (I/O) invariants for second-order systems are motivated and defined, Based on these, direct second-order balancing methods are developed, This leads naturally to direct second-order form analogs for the web-known first-order form balance and truncate model reduction method. Explicit algorithms are given throughout the paper.