On stability and controllability of multi-agent linear systems

Recent advances in communication and computing have made the control and coordination of dynamic network agents to become an area of multidisciplinary research at the intersection of the theory of control systems, communication and linear algebra. The advances of the research in multi-agent systems are strongly supported by their critical applications in different areas as for example in consensus problem of communication networks, or formation control of mobile robots. Mainly, the consensus problem has been studied from the point of view of stability. Nevertheless, recently some researchers have started to analyze the controllability problems. The study of controllability is motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. Therefore, it is meaningful to analyze how to improve the controllability of a multi-agent system. In this work we analyze the stability and controllability of multiagent systems consisting of k + 1 agents with dynamics x¿i = Aixi + Biui, i = 0, 1, . . . , kPostprint (published version

Analysis of functional output-controllability of time-invariant Composite linear systems

Small perturbations of simple eigenvalues with a change of parameters is a problem of general interest in applied mathematics. The aim of this work is to study the behavior of a simple eigenvalue of singular linear system family E(p)x'_ = A(p)x + B(p)u; y = C(p)x smoothly dependent on real parameters p = (p1,..., pn).Postprint (published version

Output observability of time-invariant singular linear systems

In this paper finite-dimensional singular linear discrete-time-invariant systems in the form Ex(k + 1) = Ax(k) + Bu(k), y(k) = Cx(k) where E;A 2 M = Mn(C), B 2 Mn£m(C), C 2 Mp£n(C), describing convolutional codes are considered and the notion of output observability is analyzed.Postprint (published version

Perturbation analysis of simple eigenvalues of singular linear systems

In this work a study of the behavior of a simple eigenvalue of singular linear system family E ( p )_ x = A ( p ) x + B ( p ) u , y = C ( p ) x smoothly dependent on a vector of real parameters p = ( p 1 ;:::;p n ) is pre- sentedPostprint (published version

Controllability of time-invariant singular linear systems

We consider triples of matrices (E; A;B), representing singular linear time invariant systems in the form Ex_ (t) = Ax(t) + Bu(t), with E;A 2 Mn(C) and B 2 Mn£m(C), under proportional and derivative feedback. Structural invariants under equivalence relation characterizing singular linear systems are used to obtain conditions for controllability of the systems.Postprint (published version

Analysis of behavior of the eigenvalues and eigenvectors of singular linear systems

Let E(p)x˙ = A(p)x + B(p)u be a family of singular linear systems smoothly dependent on a vector of real parameters p = (p1, . . . , pn). In this work we construct versal deformations of the given differentiable family under an equivalence relation, providing a special parametrization of space of systems, which can be effectively applied to perturbation analysis. Furthermore in particular, we study the behavior of a simple eigenvalue of a singular linear system family E(p)x˙ = A(p)x + B(p)u.Postprint (published version

Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system familyPostprint (published version

Analysis of behavior of a simple eigenvalue of singular system

Small perturbations of simple eigenvalues with a change of parameters is a problem of general interest in applied mathematics. The aim of this work is to study the behavior of a simple eigenvalue of singular linear system family E(p)x' = A(p)x + B(p)u; y = C(p)x smoothly dependent on real parameters p = (p1,...,pn).Postprint (published version

Testing functional output-controllability of time-invariant singular linear systems

After introducing the concept of functional output- controllability for singular systems as a generalization of the concept that is known for standard systems. This paper deals with the description of a new test for cal- culating the functional output-controllability character of finite-dimensional singular linear continuous-time- invariant systems in the form E _ x ( t ) = Ax ( t ) + Bu ( t ) y ( t ) = Cx ( t ) } (1) where E, A ∈ M = M n ( C ) , B ∈ M n m ( C ) , C ∈ M p n ( C ) . The functional output-controllability character is computed by means of the rank of a certain constant matrix which can be associated to the systemPostprint (published version

Herramientas de álgebra lineal para la ingeniería. Problemas resueltos

Postprint (published version