Physics‐Aware Observer Design for Modern Dynamical Systems: Algorithms, Fault Detection, and Practical Applications

This paper proposes a comprehensive and physics aware unified framework for observer design in modern dynamical systems, explicitly accounting for physical and engineering constraints such as actuator dynamics, state coupling, modeling uncertainties, and measurement noise. The proposed approach unifies high gain, adaptive, sliding mode, interval, and learning based observers into a coherent methodology, by systematically embedding physical insights and structural system properties into the observer synthesis process. Sufficient conditions for stability, asymptotic and exponential convergence, robustness to disturbances, and accurate fault reconstruction are rigorously derived using Lyapunov based analysis and constructive design tools. The framework is motivated by the limitations of classical observer designs when applied to heterogeneous, nonlinear, and networked systems, and provides a unifying alternative to stochastic filtering, moving horizon estimation, and purely data driven approaches by offering strong analytical guarantees and implementation transparency. Efficient computational algorithms are developed to enable real time implementation, including distributed and scalable architectures suitable for networked and multi agent systems. The applicability of the proposed framework is demonstrated through representative simulation studies involving nonlinear, cyber physical, and networked dynamical systems, where rapid convergence, robustness to uncertainties, and precise fault detection are achieved. Simulation results, presented concisely in tabular form, demonstrate rapid convergence, robustness to uncertainties, and precise fault detection, highlighting the superior performance of the proposed framework compared to existing observer design methods. These results emphasize the scientific novelty of the proposed unification strategy and its relevance for advancing both the theoretical foundations and practical deployment of observers in complex engineering systems. MSC2020 Classification: 93B52, 93C10, 93C15, 93C20.