Semi-global observer-based nonnegative edge-consensus of linear discrete-time multi-agent systems with nonnegative constraint and input saturation

Further Improvements on Non-Negative Edge Consensus of Networked Systems

In this article, the non-negative edge consensus problem is addressed for positive networked systems with undirected graphs using state-feedback protocols. In contrast to existing results, the major contributions of this work included: 1) significantly improved criteria of consequentiality and non-negativity, therefore leading to a linear programming approach and 2) necessary and sufficient criteria giving rise to a semidefinite programming approach. Specifically, an improved upper bound is given for the maximum eigenvalue of the Laplacian matrix and the (out-) in-degree of the degree matrix, and an improved consensuability and non-negativevity condition is obtained. The sufficient condition presented only requires the number of edges of a nodal network without the connection topology. Also, with the introduction of slack matrix variables, two equivalent conditions of consensuability and non-negativevity are obtained. In the conditions, the system matrices, controller gain, as well as Lyapunov matrices are separated, which is helpful for parameterization. Based on the results, a semidefinite programming algorithm for the controller is readily developed. Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work.

H∞ Control for Observer-Based Non-Negative Edge Consensus of Discrete-Time Networked Systems

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an H_∞ control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

Positive edge consensus of networked systems with input saturation

This paper studies the edge consensus problems of undirected networked systems with positivity constraint and input saturation. Based on a given nodal network, the definition of edge network is introduced, and the edge dynamics is described by positive systems subject to input saturation. With the connections between the edge network and the nodal network, the lower and upper bounds of the nonzero eigenvalues of the edge Laplacian matrix are presented. Rigorous convergence analysis is carried out. Based on the special properties of positive systems, sufficient conditions of positive edge consensus with input saturation are given without using global topology information, that is, the topology information in the given results only relates to the edge and vertex number of the nodal network. Furthermore, the nonnegative edge consensus problem with uncertain parameters is also studied based on the properties of Metzler matrix. Different from many consensus problems with input saturation which achieve semi-global consensus, the results in this paper are global consensus. The feedback matrix can be computed by solving linear matrix inequality. Some illustrative numerical and practical simulation examples are finally introduced to verify the proposed methods in this paper.