Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

This article develops a digital redesign (DR) technique for sampled-data observer-based output-feedback control of a continuous-time linear system with nonlinear perturbation. It is assumed that the nonlinear perturbation is a locally Lipschitz function. To deal with the discrete-time modelling error in nonlinear systems, as opposed to the previous approach, the DR problem is configured as a stabilisation one for error dynamics between the closed-loop system of nominal linear model under an analogue state-feedback controller and that of the linear system with the nonlinear perturbation under a sampled-data output-feedback controller. A constructive DR condition is formulated in the format of linear matrix inequalities. The stability of the actual sampled-data control system is guaranteed within the DR procedure. The effectiveness of the proposed DR methodology is demonstrated through a numerical simulation.