Stabilization of Differential Repetitive Processes

Abstract

Differential repetitive processes are a subclass of 2D systems that arise in modeling
physical processes with identical repetitions of the same task and in the analysis of other
control problems such as the design of iterative learning control laws. These models have
proved to be efficient within the framework of linear dynamics, where control laws designed in
this setting have been verified experimentally, but there are few results for nonlinear dynamics.
This paper develops new results on the stability, stabilization and disturbance attenuation,
using an H? norm measure, for nonlinear differential repetitive processes. These results are
then applied to design iterative learning control algorithms under model uncertainty and sensor
failures described by a homogeneous Markov chain with a finite set of states. The resulting
design algorithms can be computed using linear matrix inequalities.

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Identifiers

ORCID for E Rogers: orcid.org/0000-0003-0179-9398

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