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This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies. [ABSTRACT FROM AUTHOR]

This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well. [ABSTRACT FROM AUTHOR]

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This article aims to design proportional-derivative (PD) controllers for interval positive linear systems in the continuous-time domain, which still remains a widely-discussed open problem in positive systems theory. The specific objective is to design a PD controller for the system with interval uncertain parameters and time-varying delay, which simultaneously ensures closed-loop system stability and preserves positivity. The work proposes a systematic framework, with the aim of finding PD controller gains for positive robust stabilization. The methodology and algorithm are presented first in the study, and the performance of such methods is instantiated by numerical examples. [ABSTRACT FROM AUTHOR]

This note deals with the positivity-preserving consensus problem for undirected positive multiagent systems. The case that all agents have identical positive state-space models with multiple inputs is investigated. Using positive systems theory and analyzing the properties of the overall closed-loop system, positivity-preserving consensus conditions are derived. In order to preserve the positivity property of the agents, two conditions for positivity-preserving consensus are obtained. In contrast to some existing works that only give sufficient conditions for the solution, necessary and sufficient conditions are provided in this note. Then, the corresponding algorithm is developed for solution. Simulations are used to illustrate the effectiveness of the theoretical results and proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the positive edge consensus of nodal networks with Luenberger observer-based dynamic output-feedback controllers. The line graph of a nodal network, which is used to model the interaction among edges, is directed and assumed to contain a spanning tree. Based on the results in graph theory and positive systems theory, positive edge consensus problem is analyzed and the protocol design condition is given. Moreover, a semi-definite programming algorithm is developed to solve the positive edge consensus problem. Compared with the recent work [24] where the nodal graph is assumed to be strongly connected and balanced, we study the positive edge consensus problem in a more general case, where the line graph is assumed to contain a spanning tree. Finally, the numerical simulations are given to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]