On Assigning the Derivative of a Disturbance Attenuation Control Lyapunov Function

Abstract.

We consider feedback design for nonlinear, multi-input affine control systems with disturbances and present results on 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 ℒ₂ 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. A dynamic control strategy for linear systems with bounded controls is discussed in detail.