Dynamic solution of the Hamilton-Jacobi inequality in the L 2-disturbance attenuation problem

A well-established methodology to solve the disturbance attenuation problem exploits the solution of a Hamilton-Jacobi (HJ) partial differential inequality, which may be, however, difficult to solve in practical situations. Herein this drawback is resolved determining a dynamic solution of the HJ inequality, considering the immersion of the nonlinear system into an extended state-space in which a positive definite storage function can be constructed. This results in a methodology to design a dynamic controller to achieve L 2-disturbance attenuation and stability without solving any partial differential equation or inequality.