Nonlinear Sampled-Data Control Systems: Stability Theorem via Commutativity of Linearization and Discretization

In this study, we propose a local stability theory for sampled-data systems employing Lyapunov's indirect method. Our proposed method focuses on the relationship between exact discretization and linear approximation, demonstrating the feasibility of deriving an approximate model of the sampled-data system without directly solving the differential equations. We demonstrate that the local stability of the approximate model coincides with that of the sampled-data system. Consequently, by designing a controller that stabilizes this model, we can effectively stabilize the sampled-data system. The proposed theory can be utilized in the same manner as Lyapunov's indirect method in continuous-time systems, making it an easily manageable approach.