Nonlinear dynamic analysis plays a crucial role in process system engineering research, aiding in understanding system boundaries, instabilities, and optimization. However, current literature lacks a systematic approach to quantifiably analyze nonlinear dynamics in chemical processes. This work aims to fill this gap by formulating theoretical concepts and practical implementation methods for dynamic operability analysis. Dynamic operability mapping, essential for process optimization and control, faces challenges in handling dynamic systems due to the exponential increase in possible input combinations over time intervals. A novel linear time-invariant dynamic system approach and a subsequent expansion to nonlinear processes are proposed. Additionally, adaptations of dynamic operability are introduced, including a grey-box model identification algorithm that integrates Bayesian calibration for process control, and a self-stabilizing economic nonlinear model predictive controller formulation that utilizes Lyapunov functions to incorporate steady-state optimal conditions.

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