Iterative, Small-Signal L2 Stability Analysis of Nonlinear Constrained Systems

This paper provides a method to analyze the small-signal L2 gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the L2 gain are found on a bounded, compact set's...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Lavaei, Reza, Bridgeman, Leila J
Format: Article
Language:English
Subjects:
Iterative methods
L2 gain
Nonlinear control
Nonlinear systems
Robustness (mathematics)
Stability analysis
Triangulation
Upper bounds
Online Access:Get full text
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Summary:This paper provides a method to analyze the small-signal L2 gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the L2 gain are found on a bounded, compact set's triangulation. Then, to ensure that the state does not escape this set, a barrier function is found that is robust to small-signal inputs. Small-signal L2 stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The bound on the inputs is also found while searching for a barrier function. The method's effectiveness is shown in a numerical example.
ISSN:2331-8422