On Robustification of Sampled-Data Dynamic Output-Feedback Stabilizers for Control-Affine Nonlinear Systems

Abstract

In this paper, the robust sampled–data stabilization of nonlinear systems is investigated. In particular, a methodology for the design of robust sampled–data Dynamic Output Feedback Controllers (DOFCs) is provided for control–affine nonlinear systems affected by actuation disturbances and measurement errors. The notion of dynamic output steepest descent feedback, continuous or not, induced by suitably Control Lyapunov functions is used together with the ISS redesign methodology for the development of the proposed robust sampled–data stabilizer. Under the assumption that the actuation disturbances and measurement errors are bounded with a–priori known bounds and that the measurement error affects marginally the control term designed via the ISS redesign methodology it is proved that: there exists a suitably fast sampling such that the proposed sampled–data DOFC yields semi–global practical stability of the related closed–loop system regardless of the above actuation disturbances and measurement errors. In the methodology here proposed, time–varying sampling periods are allowed and the intersampling system behaviour is taken into account. The provided results are validated on a chemical reactor system.