On output stabilizability of differential–algebraic equations

Abstract

We study output stabilizability of differential–algebraic systems. Two different notions of stability, an asymptotic one and one based on the L q norm of the output are compared and shown be equivalent. To introduce the use of the main concepts of output injection and the Kalman observability decomposition, we begin with a short proof of the result for the special case of ordinary differential equations. These results can then be generalized to differential–algebraic equations, which requires some further attention, especially with respect to observability. Equivalence of the two output stabilizabilities is worth knowing in its own right, and has applications for example in the context of optimal control.