Theory# State Space Model of Structural Dynamics Partitioned Equation of Dynamic Equilibrium Equation of Motion Continuous LTI State-Space Representation Discrete LTI State-Space Representation Modal Properties from State Space Realization Eigendecompositions of \(\mathbf{A}_{c}\) and \(\mathbf{A}\) Natural Frequencies and Modal Damping Ratios Mode Shapes Eigensystem Realization Algorithm (ERA) Observer Kalman Filter Identification (OKID) System Realization by Information Matrix (SRIM) Discrete-Time System Matrix Equation Observability Matrix from Information Matrix State Equation Matrices from Observability Matrix Appendix: Manipulation of discrete-time system matrix equation into correlation matrix relationships