Passivity-Based Control of Sampled-Data Systems on Lie Groups with Linear Outputs
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Date
2016-12-22
Authors
McCarthy, Philip James
Nielsen, Christopher
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
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.
Description
The 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/
Keywords
nonlinear control, discrete-time systems, stabilization, Lie groups, passivity