Closed-Form Gramians and Riccati Solutions for Reduced Second-Order Energy-System Benchmarks
Reduced circuit and electromechanical models often lead to the scalar second-order system ay″+by′+cy=u(t). General controllability, minimum-input-energy, and LQR results for such systems are standard; the contribution here is an explicit specialization that exploits the companion-matrix decomposition A=μI+B, B2=ηI. Thi...