1,474 research outputs found
Zero forcing sets and controllability of dynamical systems defined on graphs
In this paper, controllability of systems defined on graphs is discussed. We
consider the problem of controllability of the network for a family of matrices
carrying the structure of an underlying directed graph. A one-to-one
correspondence between the set of leaders rendering the network controllable
and zero forcing sets is established. To illustrate the proposed results,
special cases including path, cycle, and complete graphs are discussed.
Moreover, as shown for graphs with a tree structure, the proposed results of
the present paper together with the existing results on the zero forcing sets
lead to a minimal leader selection scheme in particular cases
Controllability and observability of grid graphs via reduction and symmetries
In this paper we investigate the controllability and observability properties
of a family of linear dynamical systems, whose structure is induced by the
Laplacian of a grid graph. This analysis is motivated by several applications
in network control and estimation, quantum computation and discretization of
partial differential equations. Specifically, we characterize the structure of
the grid eigenvectors by means of suitable decompositions of the graph. For
each eigenvalue, based on its multiplicity and on suitable symmetries of the
corresponding eigenvectors, we provide necessary and sufficient conditions to
characterize all and only the nodes from which the induced dynamical system is
controllable (observable). We discuss the proposed criteria and show, through
suitable examples, how such criteria reduce the complexity of the
controllability (respectively observability) analysis of the grid
Structural Completeness of a Multi-channel Linear System with Dependent Parameters
It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of
a multi-channel linear system plays a central role in the stabilization of such
a system with decentralized control. A parameterized multi-channel linear
system is said to be "structurally complete" if it has no fixed spectrum for
almost all parameter values. Necessary and sufficient algebraic conditions are
presented for a multi-channel linear system with dependent parameters to be
structurally complete. An equivalent graphical condition is also given for a
certain type of parameterization
Zero forcing number, constrained matchings and strong structural controllability
The zero forcing number is a graph invariant introduced to study the minimum
rank of the graph. In 2008, Aazami proved the NP-hardness of computing the zero
forcing number of a simple undirected graph. We complete this NP-hardness
result by showing that the non-equivalent problem of computing the zero forcing
number of a directed graph allowing loops is also NP-hard. The rest of the
paper is devoted to the strong controllability of a networked system. This kind
of controllability takes into account only the structure of the interconnection
graph, but not the interconnection strengths along the edges. We provide a
necessary and sufficient condition in terms of zero forcing sets for the strong
controllability of a system whose underlying graph is a directed graph allowing
loops. Moreover, we explain how our result differs from a recent related result
discovered by Monshizadeh et al. Finally, we show how to solve the problem of
finding efficiently a minimum-size input set for the strong controllability of
a self-damped system with a tree-structure.Comment: Submitted as a journal paper in May 201
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