Graph-theoretic approach to symbolic analysis of linear descriptor systems

AbstractContinuous descriptor systems EẋAx+Bu, yCx, where E is a possibly singular matrix, are symbolically analyzed by means of digraphs. Starting with four different digraph characterizations of square matrices and determinants, the author favors the Cauchy-Coates interpretation. Then, an appropriate digraph representation of the matrix pencil (sE−A) is given, which is followed by a digraph interpretation of det(sE−A) and the transfer-function matrix C(sE−A)−1B. Next, a graph-theoretic procedure is derived to reveal a possibly hidden factorizability of the determinant det(sE−A). This is very important for large-scale systems. Finally, as an application of the derived results, an electrical network is analyzed symbolically

Controllability of linear differential-algebraic systems - A survey

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients. Regularity, which is, loosely speaking, a concept related to existence and uniqueness of solutions for any inhomogeneity, is not required in this article. The concepts of impulse controllability, controllability at infinity, behavioral controllability, strong and complete controllability are described and defined in time-domain. Equivalent criteria that generalize the Hautus test are presented and proved. Special emphasis is placed on normal forms under state space transformation and, further, under state space, input and feedback transformations. Special forms generalizing the Kalman decomposition and Brunovsky form are presented. Consequences for state feedback design and geometric interpretation of the space of reachable states in terms of invariant subspaces are proved

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived

Abordagem geométrica para estabilização por realimentação de saídas e sua extensão aos sistemas descritores

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Tecnológico. Programa de Pós-Graduação em Engenharia ElétricaEste trabalho trata os problemas de estabilização e de posicionamento regional de pólo em sistemas lineares contínuos no tempo usando realimentação estática de saídas. Os resultados apresentados têm como ponto de partida o conceito de subespaços (C,A,B)-invariantes caracterizados algebricamente através de um par de equações acopladas de Sylvester, cuja solução pode ser obtida, para sistemas que verificam a condição de Kimura (m+ p >n), em duas etapas utilizando o algoritmo de Syrmos e Lewis.No caso de sistemas normais, é demonstrado que subespaços (C,A,B)-invariantes estabilizáveis por saídas podem ser caracterizados através de equações acopladas de Lyapunov. Baseada nessas equações, é proposta uma condição necessária e suficiente para a existência de solução do problema de estabilização por realimentação estática de saídas. Para sistemas satisfazendo a condição de Kimura, são propostos dois algoritmos ( primal e dual) para solução das equações acopladas de Lyapunov. A técnica de estabilização é então adaptada para tratar o problema de posicionamento regional de pólos