On assigning the derivative of a disturbance attenuation control Lyapunov function

We consider feedback design for nonlinear, multi-input affine control syste ms with disturbances and present results on assigning, by choice of feedbac k, a desirable upper bound to a given control Lyapunov function (clf) candi date's derivative along closed-loop trajectories. Specific choices for the upper bound are motivated by L-2 and L-infinity disturbance attenuation pro blems. The main result leads to corollaries on "backstepping" locally Lipsc hitz disturbance attenuation control laws that are perhaps implicitly defin ed through a locally Lipschitz equation. The results emphasize that only ro ugh information about the elf is needed to synthesize a suitable controller . A dynamic control strategy for linear systems with bounded controls is di scussed in detail.