Structural Controllability Of Linear Systems Research Articles

A Unifying Framework for Strong Structural Controllability

This article deals with strong structural controllability of linear systems. In contrast to the existing work, the structured systems studied in this article have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices, whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph-theoretic condition for the full rank property of a given pattern matrix. This graph-theoretic condition makes use of a new color change rule that is introduced in this article. Based on these two results, we then establish a necessary and sufficient graph-theoretic condition for strong structural controllability. Moreover, we relate our results to those that exist in the literature and explain how our results generalize previous work.

A MATLAB Toolbox for Structural Analysis of Linear Systems

Abstract We present a MATLAB toolbox with several well-known algorithms to test the structural and strong structural controllability of linear systems. For structural controllability a function to determine the dimension of the structurally reachable subspace and a function for calculating the generic rank of a matrix are provided. The strong structural controllability functions are based on different algorithms, where one of the algorithms has a linear time complexity. Additionally the toolbox provides functions to handle uncertain systems and signed systems. To check the correctness and performance of the functions several test scripts are included. The help browser provides additional information to the user. The toolbox is useful for analyzing structured systems given in state space form. It may also be used for teaching the methods of structural analysis. It is intended to expand the toolbox with further algorithms for structural analysis.

Impact of the actuator failures on the structural controllability of linear systems: a graph theoretical approach

This study is concerned with the impact of components’ failure on the controllability of an automated system when operating. The work proposes a method based on a graph-theoretic approach to study the controllability of systems whose only the structure is known. The study focuses on the actuators’ failures and assumes that their probabilities are known. The controllability conditions are first recalled for a linear system. One study’s originality is to express the property as a Boolean equation of the actuators’ set involved in the condition. A second originality of the study is to extend the definition of the reliability to cover structural properties like the controllability and to assess the probability to conserve or to lose it from the components’ reliability.