Stability of Integral Delay Equations and Stabilization of Age-Structured Models
Abstract
We present bounded dynamic (but observer-free) output feedback laws that achieve global stabilization of equilibrium profiles of the partial differential equation (PDE) model of a simplified, age-structured chemostat model. The chemostat PDE state is positive-valued, which means that our global stabilization is established in the positive orthant of a particular function space-a rather non-standard situation, for which we develop non-standard tools. Our feedback laws do not employ any of the (distributed) parametric knowledge of the model. Moreover, we provide a family of highly unconventional Control Lyapunov Functionals (CLFs) for the age-structured chemostat PDE model. Two kinds of feedback stabilizers are provided: stabilizers with continuously adjusted input and sampled-data stabilizers. The results are based on the transformation of the first-order hyperbolic partial differential equation to an ordinary differential equation (one-dimensional) and an integral delay equation (infinite-dimensional). Novel stability results for integral delay equations are also provided; the results are of independent interest and allow the explicit construction of the CLF for the age-structured chemostat model.
Keywords
Cite
@article{arxiv.1609.09437,
title = {Stability of Integral Delay Equations and Stabilization of Age-Structured Models},
author = {Iasson Karafyllis and Miroslav Krstic},
journal= {arXiv preprint arXiv:1609.09437},
year = {2016}
}
Comments
54 pages, 4 figures, submitted to ESAIM COCV for possible publication