Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

On the edge: Southern Levantine Epipalaeolithic–Neolithic chronological succession

The broad picture of the cultural and chronological succession from the Epipalaeolithic to the Neolithic in the southern Levant is generally well understood. However, at a more detailed, local level, many questions remain unanswered. In this paper we examine the archaeological record of cultural developments in southern Jordan and the Negev. Focusing on a series of 14C dates from the early occupation of the PPNA site of WF16, we provide a critical review of dating evidence for the region. This review suggests that while the 14C chronology is ambiguous and problematic there is good evidence for a local historical development from the Harifian variant of the Natufian to the early PPNA, well to the south of any core Mediterranean woodland zone. This stresses the importance of considering developments at local scales of analysis, and that the Neolithic transition occurred within a framework of many interacting sub-regional provinces.

Regularization of time-varying descriptor systems by the asvd

We study linear variable coefficient control problems in descriptor form. Based on a behaviour approach and the general theory for linear differential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system.