When Is a Nonlinear System Semiglobally Asymptotically Stabilizable by Digital Feedback?

For multi-input-multi-output (MIMO) nonlinear systems, we prove that while global asymptotic stabilizability may not ensure semiglobal asymptotic stabilizability (SGAS) by sampled-data state feedback, global asymptotic plus local exponential stabilizability (GALES) does imply the existence of an SGAS sampled-data state feedback controller. Based on this result, we further prove the main contribution of this article: GALES and uniform observability imply SGAS by sampled-data output feedback, which is indeed a hybrid version of the “separation principle” for nonlinear systems. The development of the “digital separation principle” is made possible by employing a subtle Lyapunov argument that makes the estimation of domains of attraction and semiglobal asymptotic analysis relatively intuitive and simple, without involving intricate Lyapunov functions and the corresponding level sets. Results on SGAS by sampled-data feedback for representative classes of nonlinear systems are also given as illustrations.