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In this article, we refocus on the distributed observer construction of a continuous-time linear time-invariant (LTI) system, which is called the target system, by using a network of observers to measure the output of the target system. Each observer can access only a part of the component information of the output of the target system, but the consensus-based communication among them can make it possible for each observer to estimate the full state vector of the target system asymptotically. The main objective of this article is to simplify the distributed reduced-order observer design for the LTI system on the basis of the consensus communication pattern. For observers interacting on a directed graph, we first address the problem of the distributed reduced-order observer design for the detectable target system and provide sufficient conditions involving the topology information to guarantee the existence of the distributed reduced-order observer. Then, the dependence on the topology information in the sufficient conditions will be eliminated by using the adaptive strategy and so that a completely distributed reduced-order observer can be designed for the target system. Finally, some numerical simulations are proposed to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the positive edge consensus problems for undirected networks, where each edge is modeled by a continuous-time positive system with sector input nonlinearities. Based on a given nodal network, the corresponding edge network is presented, and some relationships between the given nodal network and its edge network are given. The observer-based protocol for non-negative consensus is proposed. Rigorous theoretical analysis which considers both the input nonlinearities and the positivity constraint is introduced to achieve a global consensus result. Simultaneous stabilization problems are constructed for edge-based non-negative consensus using the maximum and the minimum nonzero eigenvalues of the edge Laplacian matrix. Furthermore, the robustness of the positive edge consensus to parameter perturbation is illustrated. Sufficient non-negative consensus conditions related to the bounds of system matrices are given, and the non-negative edge consensus conditions for star nodal networks are also given only using the vertex number. Iterative linear matrix inequalities (LMIs)/LMI algorithm is presented to obtain the feedback matrix and the observer matrix. The given theoretical results are finally illustrated by some simulations. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for directed positive multiagent systems with nonlinear control input. The directed topology is supposed to be strongly connected. For the case of sector input nonlinearities, the non-negative global consensus conditions are presented by using a novel analysis method which directly considers the nonlinear input, and the feedback matrices are obtained with convex optimization method by solving the quadratic matrix inequalities subject to non-negative constraints. For the case of saturation-type sector input nonlinearities, the global consensus and local consensus results are analyzed, respectively. With the properties of Metzler matrix, the non-negative consensus results are further extended to the strongly connected and balanced positive multiagent systems subject to (saturation-type) sector input nonlinearities and parameter uncertainties. The results are simplified, and the feedback matrices can be given by solving iterative linear matrix inequality with non-negative constraints. Two simulation examples and a practical electrical circuit model are finally carried out to verify the proposed control schemes. [ABSTRACT FROM AUTHOR]