Incremental Gain Computation and Regulation of Discrete-time Positive Luré Systems using Linear Programming
Journal:
arXiv
Published Date:
May 30, 2025
Abstract
This work approaches the problem of computing incremental $\ell_1$ and
$\ell_\infty$ gains for discrete-time positive systems in \lure feedback with
static memoryless nonlinearities, and regulating the $\ell_\infty$ gain through
the design of a state-feedback controller. Finite incremental gains provide a
quantitative measure of robustness for trajectories, and will ensure that all
pairs of trajectories will converge to a fixed point or will diverge together
in the absence of an applied input. Upper-bounds on these incremental gains can
be computed through linear programming. Computation and regulation of the
$\ell_1$ and $\ell_\infty$ incremental gains are verified by numerical
examples.
