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.2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. P. Di Franco, G. Scarciotti, and A. Astolfi, "A Disturbance Attenuation Approach for the Control of Differential-Algebraic Systems," IEEE Conference on Decision and Control (CDC), Miami Beach, FL, December 2018, pp. 4695-4700. doi: 10.1109/CDC.2018.8619786