Semiglobal stabilization of linearly uncontrollable and unobservable nonlinear systems via sampled‐data control

Abstract

SummaryThis article investigates the problem of using sampled‐data state/output feedback to semiglobally stabilize a class of uncertain nonlinear systems whose linearization around the origin is neither controllable nor observable. For any arbitrarily large bound of initial states, by employing homogeneous domination approach and a homogeneous version of Gronwall‐Bellman inequality, a sampled‐data state feedback controller with appropriate sampling period and scaling gain is constructed to semiglobally stabilize the system. In the case when not all states are available, a reduced‐order sampled‐data observer is constructed to provide estimates for the control law, which can guarantee semiglobal stability of the closed‐loop system with carefully selected sampling period and scaling gain.