Linear-quadratic infinite time horizon optimal control for differential-algebraic equations - a new algebraic criterion

with x0 ∈ R, B ∈ R and E,A ∈ R, such that the pencil sE − A ∈ R[s] is regular, that is, det(sE −A) 6= 0. For systems governed by ordinary differentialequations (that is, E is the identity matrix), a rigorous analysis of this problem has its origin in the 60s of the 20th century [6, 8–10, 13, 15, 21]. In particular, the article [20] by Willems gives a complete characterization of linear-quadratic optimal control of ordinary systems by means of solvability of an associated algebraic Riccati equation and feasibility of a certain linear matrix inequality. Mainly two approaches to the generalization of this theory exist for the differential-algebraic case: The articles [11,12,14] by Kawamoto et al. and Kurina on the one hand, and [4] by Bender and Laub on the other hand introduce different