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Disturbance Attenuation in Control Systems

The paper deals with standard mathematical models for nonlinear affine control systems with two (vector-valued) inputs u (=control) and w (unknown except for a bound for the sup-norm). Interpretation of this scenario and its wide range of applications (in control and differential game theory): See the introduction. The main result of the paper is the presentation of a dissipation equality which seems to be new and which is the result of a special control strategy (discretized state feedback, see the introduction). Combination with Lyapunov techniques leads to a concrete proposal for stabilizing disturbed control system. The mathematical background — which is worked out in detail — amounts to an explicit integration of the Hamilton-Jacobi partial differential equation via the method of characteristics.