This chapterMKC system presents a comprehensive analysis of controllability and observability in large-scale mass–stiffness–damping systemsMass–stiffness–damping system (MKC systemsMKC system), a class of dynamic models critical to mechanical, aerospace, and structural engineering. BuildingBuilding on classical state-space theory and the foundational work of Kalman, the chapter explores both traditional and structural criteria for analyzing these key qualitative properties. By transforming second-order differential models into state-space form, it introduces practical methods to assess system controllability and observability using controllability and observability matricesObservability matrix, GramiansGramian, and rank conditions. A simplified criterion tailored to MKC systemsMKC system is derived, significantly reducing computational complexityComputational complexity by focusing on the rank of augmented matricesAugmented matrix involving physical parameters (M, K, C) and the input matrix. The chapter also explores structural controllabilityStructural controllability through Boolean matrixBoolean matrix theory and graph-based algorithms, providing efficient tools for analyzing large systems where numerical methods may fail due to ill-conditioningIll-conditioning. Rotor-bearing systems with cross-coupled stiffness and damping are used as a case study, illustrating the general structural controllabilityStructural controllability of such systems. The chapter concludes by emphasizing the duality between controllability and observability, offering a foundation for extending these methods to observability analysis. Overall, it equips engineers with both theoretical insight and computational tools for robust control design in complex MKC systemsMKC system.