Iterative, local, small-signal L2 stability analysis of nonlinear constrained systems

This paper provides a method to analyze the local, 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 local L2-gain are found on a bounded, compact set's triangulation. Then, to ensure that the state does not escape this set, a continuous piecewise affine barrier function is found that is robust to small-signal inputs. Local, small-signal L2 stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The method's effectiveness is shown in a numerical example.

Duke Scholars

Author Leila Bridgeman Thomas Lord Department of Mechanical Engineering and Materia ...