A Disturbance Attenuation Approach for the Control of Differential-Algebraic Systems

In this paper the problem of controlling differential-algebraic systems with index-1 is addressed. The proposed technique is based on the interpretation of differential-algebraic systems as the feedback interconnection of a differential system and an algebraic system. In this framework, the algebraic variable can be treated as an external disturbance acting on the differential system. A direct consequence of this approach is that the control problem reduces to a classical disturbance attenuation problem with internal stability. We also show that the application of the proposed theory to the linear case yields classical results. Finally, an example inspired by an air suspension system in a truck illustrates the technique.

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