Output feedback event-based control of time-varying nonlinear systems

In this paper, the stabilization problem of time-varying nonlinear systems through digital event-triggered output feedback controllers is addressed. In particular, a methodology for the design of quantized sampled-data observer-based event-triggered controllers is proposed for time-varying nonlinear systems not necessarily affine in the control input. The proposed methodology is based on the notion of Dynamic Output Steepest Descend Feedback (DOSDF) which is here properly modified to cope with the case of digital event-triggered output feedback controllers and time-varying nonlinear systems. Then, the stabilization in the sample-and-hold sense theory is suitably exploited as a tool to prove that, under sufficiently fast sampling and accurate quantization of the input/output channels, the quantized sampled-data implementation of DOSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical stability property of the corresponding digital closed-loop system. Discontinuities in the functions describing the DOSDF at hand are allowed. Moreover, the cases of time-varying sampling periods and of non-uniform quantization of both input/output channels are included in the theory here developed. An application of the proposed methodology in the context of the well-known Sontag’s universal formula is also presented. Moreover, the proposed results are validated through applications concerning: (i) a particular class of time-varying nonlinear systems; (ii) a glucose-insulin system; (iii) a class of time-varying nonlinear systems not affine in the control input.