Controllability and Stabilizability of Networks of Linear Systems

We provide necessary and sufficient conditions for the node systems, the graph adjacency matrix, and the input matrix such that a heterogeneous network of multi-input multi-output linear time-invariant (LTI) node systems with constant linear couplings is controllable or stabilizable through the external input. We also provide specializations of these general conditions for homogeneous networks. Finally, we give a very simple, necessary and sufficient condition under which a homogeneous network of single-input single-output LTI node systems is stable in the absence of the external input

Consensus stabilizability and exact consensus controllability of multi-agent linear systems

A goal in engineering systems is to try to control them. Control theory offers mathematical tools for steering engineered systems towards a desired state. Stabilizability and controllability can be studied under different points of view, in particular, we focus on measure of controllability in the sense of the minimum set of controls that need for to steer the multiagent system toward any desired state. In this paper, we study the consensus stabilizability and exact consensus controllability of multi-agent linear systems, in which all agents have a same linear dynamic mode that can be in any orderPostprint (published version

Stabilization over power-constrained parallel Gaussian channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of H2 control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoder

A Unifying Framework for Strong Structural Controllability

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper 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 paper. 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 exists in the literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure