On assigning the derivative of a disturbance attenuation CLF

This paper considers feedback design for nonlinear, multi-input affine control systems with disturbances. It studies the problem of assigning, by choice of feedback, a desirable upper bound to a given control Lyapunov function (CLF) candidate´s derivative along closed-loop trajectories. Specific choices for the upper bound are motivated by L ₂ and L_∞ disturbance attenuation problems. The main result leads to corollaries on “backstepping” locally Lipschitz disturbance attenuation control laws that are perhaps implicitly defined through a locally Lipschitz equation. The results emphasize that only rough information about the CLF is needed to synthesize a suitable controller