ThisModel identification chapter presents a systematic and unified frameworkUnified framework for the identification of dynamic system models, a foundational step in the design of effective control systems. In industrial applications, where system complexities and parameter uncertainties challenge traditional modeling, the use of estimatedLumped-parameter model lumped-parameter modelsLumped-parameter model becomes essential. This chapter introduces a suite of recursive least-squares (RLS)Recursive Least-Squares (RLS) algorithms for identifying both discrete- and continuous-time state-space modelsState-space model, tailored for single-input single-output (SISO) and multi-input multi-output (MIMO) systems. The chapter progresses from identifying linear difference equationsLinear difference equation to discrete-time and continuous-time state-space modelsState-space model, highlighting the practical advantages of each approach. Both direct and indirect estimation methods are explored, with emphasis on real-time adaptability, computational efficiencyComputational efficiency, and robustness in the presence of time-varying or nonlinear parametersNonlinear parameter. A key feature is the incorporation of a forgetting factorForgetting factor, allowing the algorithms to "track" parameter changes and improve estimation accuracy over time. The framework is validated through an example of a mass–stiffness–damping systemMass–stiffness–damping system (MKC systemMKC system), demonstrating high accuracy in estimating system matricesSystem matrix and facilitating model conversionModel conversion between time domainsTime domain. The techniques discussed are simple to implement, highly adaptable, and suitable for modern control applications where real-time modeling and adaptive control are critical.