Real-time structural health monitoring technique based on the interaction matrix formulation is developed in this study. New observer based methods such as ARMarkov observer and Input Error Function (IRF) observer are proposed to estimate extent of damage in real-time. Mathematical formulation for IRF based on interaction matrix formulation is developed in this study. Internal relative virtual force and equivalent system concepts are developed to establish IRF for real-time structural damage detection and localization. Input error function based structural damage detection method is applied to a three-dimensional truss structure, in which nonlinear and time-varying damage in members is detected and localized in real-time. IRF observers are proposed to estimate the extent of damage in real-time. Extent of damage is determined by minimizing the IRF. Optimization procedure proposed is robust with respect to system uncertainty and noise levels in the input-output measurements. When compared to state space observer based structural damage detection methods, in the design of ARMarkov observers, system and noise statistics are not necessary. Additionally, the method does not require initial conditions and is also robust to noisy output measurements. Furthermore, Sensitivity Enhancing Control (SEC) algorithms can be incorporated into ARMarkov observers to detect small structural damages. Proposed ARMarkov observers based on interaction matrix formulation are applied to track progressive stiffness deterioration in real-time in a two-dimensional truss structure. Experimental verification of an input failure detection algorithm is performed on a NASA 8-Bay truss structure, where, failure among the actuators is detected and distinguished in real-time. Structural damage detection methods based on ARMarkov observers and IRF observers are verified experimentally on a time varying two-degree of freedom system. Stiffness variation in this system is tracked in real-time using the proposed structural damage detection methods. IRF based structural damage detection is evaluated for structural health monitoring study of IASC-ASCE structural health monitoring benchmark problem. It is shown that the proposed formulation performs well for different damage cases established by IASC-ASCE structural health monitoring task group.