Repeated eigenstructure assignment in the computation of friends of output-nulling subspaces

This paper is concerned with the parameterisation of basis matrices and the simultaneous computation of friends of the output nulling subspaces V*, V*g and R* with the assignment of the corresponding inner and outer closed-loop free eigenstructure. Differently from the classical techniques presented in the literature so far on this topic, which are based on the standard pole assignment algorithms and are therefore applicable only in the non-defective case, the method presented in this paper can be applied in the case of closed-loop eigenvalues with arbitrary multiplicity

Robust eigenstructure assignment in geometric control theory

In this paper we employ the Rosenbrock system matrix pencil for the computation of output-nulling subspaces of linear time-invariant systems which appear in the solution of a large number of control and estimation problems. We also consider the problem of finding friends of these output-nulling subspaces, i.e., the feedback matrices that render such subspaces invariant with respect to the closed-loop map and output-nulling with respect to the output map, and which at the same time deliver a robust closed-loop eigenstructure. We show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

Linear systems and control structure selection

This thesis is concerned with the development of concepts and results to facilitate study in two areas of control methodology. The two notions investigated are measures of controllability and observability and eigenstructure assignment. The link between these two areas is exposed, and it is demonstrated how the eigenvectors of a system play an important role in determining the degree of controllability and observability. The main concerns are issues dealing with the complexity of the instrumentation, and in particular the development of techniques that may assist in the development of methodology for sensor and actuator placement. The research involves the development of notions that help to structure a system on which control design is based. There are two areas of investigation. The first is the development of concepts and tools that aid in the selection and placement of sensors and actuators based on properties related to degrees of controllability and observability. The second is the investigation of the eigenstructure of a system and its properties, which enable the development of design procedures based on eigenstructure properties. A study of existing measures of controllability and observability leads to new techniques which take into consideration the problem of coordinate transformations, which is often overlooked. It is shown that the degree of controllability is influenced by changes in the structure of the state feedback matrix, as well as how controllability properties can be determined from Pliicker matrices of transfer function matrices. It is also shown that the energy required to move a system from one state to another is linked to the singular values of the output controllability grammian. A review of the problem of eigenstructure assignment paves the way for the development of a new technique of assigning the closed loop eigenstructure. This is based on matrix fraction description algorithms, and stems from an algebraic description of the total system behaviour, leading to a systematic study of closed loop eigenvectors by using a parametric approach. A new algebraic characterisation of the family of closed loop eigenvectors and related input and output directions is shown. Closed loop system robustness to parameter variations is also considered, where it is shown that there is a link with the orthogonality of the matrix of eigenvectors. As a result, the notion of strong stability is introduced, where it is shown that the shape of the eigenframe plays a role in the system response by way of overshoots. The work develops concepts and results which are important steps in the development of an integrated methodology for input, output structure selection

On the Construction of Jordan Chains in the Eigenstructure Assignment for Output-Nulling Subspaces

© 2018 European Control Association (EUCA). This paper investigates several aspects related with the eigenstructure assignment problem for output-nulling subspaces. In particular, we deliver an alternative method for the computation of the feedback matrix that renders these subspaces invariant with respect to the closed-loop system matrix and assigns a defective eigenstructure in the closed-loop eigenstructure restricted to these subspaces. We show that this method, which consists in building the Jordan chains starting from the generalized eigenspace to the null-space of the Rosenbrock matrix, provides additional freedom in the resulting basis matrix

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

Eigenstructure assignment in linear geometric control

The focus of this paper is the connection between two foundational areas of linear time-invariant (LTI) systems theory: geometric control and eigenstructure assignment. In particular, we study the properties of the null-spaces of the reachability matrix pencil and of the Rosenbrock system matrix, which have been extensively used as two computational building blocks for the calculation of pole placing state feedback matrices and pole placing friends of output-nulling subspaces. Our objective is to show that the subspaces in the chains of kernels obtained in the construction of these feedback matrices interact with each other in ways that are entirely independent from the choice of eigenvalues. So far, these chains of subspaces have only been studied in the case of stationarity. In this case, it is known that these chains converge to the classic Kalman reachable subspace \u211b for the reachability matrix pencil and to the largest reachability subspace \u211b c6 in the case of the Rosenbrock matrix, respectively. Here we are interested in showing that even before stationarity has been reached, the partial chains are linked to structural properties of the system, and are therefore independent of the closed-loop eigenvalues that we wish to assign. We further characterize these subspaces by investigating the notion of largest subspace on which it is possible to assign the closed-loop spectrum (possibly maintaining the output at zero) without resorting to non-trivial Jordan forms