Improved Small-Signal L2 Gain Analysis for Nonlinear Systems
Abstract
TheL2-gain characterizes a dynamical system's input-output properties, but can be difficult to determine for nonlinear systems. Previous work designed a nonconvex optimization problem to simultaneously search for a continuous piecewise affine (CPA) storage function and an upper bound on the small-signal L2-gain of a dynamical system over a triangulated region about the origin. This work improves upon those results by establishing a tighter upper-bound on a system's gain using a convex optimization problem. By reformulating the relationship between the Hamilton-Jacobi inequality and L2-gain as a linear matrix inequality and then developing novel LMI error bounds for a triangulation, tighter gain bounds are derived and computed more efficiently. Additionally, a combined quadratic and CPA storage function is considered to expand the nonlinear systems this optimization problem is applicable to. Numerical results demonstrate the tighter upper bound on a dynamical system's gain.
Cite
@article{arxiv.2309.08034,
title = {Improved Small-Signal L2 Gain Analysis for Nonlinear Systems},
author = {Amy Strong and Reza Lavaei and Leila J. Bridgeman},
journal= {arXiv preprint arXiv:2309.08034},
year = {2024}
}