  The L2-gain characterizes a dynamical system's input-output properties and is
used for important control methods, like H-infinity control. However, gain 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 to establish a tighter upper-bound on a
system's gain through a convex optimization problem. By reformulating the
relationship between the Hamilton-Jacobi equations and gain as a linear matrix
inequality (LMI) and then developing novel LMI error bounds for a
triangulation, tighter gain bounds are derived and computed more efficiently.
Numerical results demonstrate the less conservative upper bound on a dynamical
system's gain.
