McCarthy, Philip JamesNielsen, Christopher2021-09-232021-09-232016-12-22https://doi.org/10.1016/j.ifacol.2016.10.299http://hdl.handle.net/10012/17486The final publication is available at Elsevier via http://dx.doi.org/https://doi.org/10.1016/j.ifacol.2016.10.299. © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We present a method of stabilizing a sampled-data system that evolves on a matrix Lie group using passivity. The continuous-time plant is assumed passive with known storage function, and its passivity is preserved under sampling by redefining the output of the discretized plant and keeping the storage function. We show that driftlessness is a necessary condition for a sampled-data system on a matrix Lie group to be zero-state observable. The closed-loop sampled-data system is stabilized by any strictly passive controller, and we present a synthesis procedure for a strictly positive real LTI controller. The closed-loop system is shown to be asymptotically stable. This stabilization method is applied to asymptotic tracking of piecewise constant references.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalnonlinear controldiscrete-time systemsstabilizationLie groupspassivityArticle