Nonlinear L2-gain verification for bilinear systems

A general class of bilinear systems is shown to satisfy a nonlinear L₂-gain property that naturally generalizes the standard (linear) L₂-gain inequality. This property is demonstrated via direct construction of appropriate transient and gain bounds, and by the application of existing dissipation-based verification results that involve the solution of a Hamilton-Jacobi-Bellman partial differential equation. An example illustrating the obtained bounds is also included, along with a discussion concerning interconnections of such systems.