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

Abstract

In this paper the problem of controlling differential-algebraic systems with index-1 is addressed. The proposed technique is based on the interpretation of differentialalgebraic 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.

Stabilization of differential-algebraic systems with Lipschitz nonlinearities via feedback decomposition

“…Continuing this line of research, in the present paper we study the stabilization of Lipschitz DAE systems. The proposed approach is based on the idea developed in [15], and extended in [16], according to which the algebraic variable is treated as an external disturbance and the DAE system is interpreted as the feedback interconnection of a nonlinear system and an algebraic system. A further extension of this concept is to consider the nonlinear terms as additional algebraic variables, reducing the stabilization problem of DAE systems with Lipschitz nonlinearities to a classical disturbance attenuation problem with internal stability for a linear system.…”