In this paper, the state estimation problem of a continuous-time liner time-invariant system is investigated for the situation with unknown external input disturbance and measurement noise. A robust distributed interval observer is designed, which consists of a group of sensors communicating with others through a directed graph where each sensor can only access partial information from the output of the plant. The communication among the sensors together with the heterogeneity and undetectability of the sensors result in some stringent requirements on the robust distributed interval observer construction. To resolve these restrictions, the internally positive representation originated from a single agent system is introduced into the robust distributed interval observer. After presenting detailed design and analysis, numerical simulations are demonstrated to verify the theoretical results.

This paper develops a new high-gain observer design method for nonlinear systems that has a lower gain compared to the standard high-gain observer. This new observer, called HG/LMI observer is obtained by combining the standard high gain methodology with the LMI-based observer design technique. Through analytical developments, the paper shows how the new observer provides lower gains, shows how it applies to systems with multi nonlinear functions and analyzes performance in the presence of measurement noise and/or delayed output measurements. A numerical example is given to illustrate the increasing advantage of the new HG/LMI observer with increase in the observer's "compromise index". Finally, the applicability and performance of the observer is demonstrated for a real-world application consisting of a train's magnetic levitation system.

In this article, we generalize the results on self-synchronization of Lur’e networks diffusively interconnected through dynamic relative output-feedback from the undirected graph case in Zhang et al. 2016 to the general directed graph case. A linear dynamic self-synchronization protocol of the same structure is adopted as the one proposed in Zhang et al. 2016. That is, the Lur’e-type nonlinearity is not involved in our self-synchronization protocol. It is in fact unknown and only assumed to be incrementally sector bounded within a given sector. In the absence of a leader Lur’e system defining the synchronization trajectory, we construct a novel self-synchronization manifold in order to derive the self-synchronization error dynamics. Meanwhile, the connectivity of the general directed graph having a directed spanning tree is quantified by the global connectivity, instead of the so-called general algebraic connectivity used in the directed graph case under static relative state feedback. The global connectivity plays a crucial role in handling self-synchronization problems of directed nonlinear networks via dynamic relative output feedback, including directed networks with the Lipschitz nonlinear node dynamics, which is also discussed in this article. The protocol parameter matrix design is performed by solving the obtained LMI conditions in sequence. In addition, some discussions are complemented on the important technical details in our self-synchronization protocol design along with extensions. Finally, our theoretical results are illustrated through numerical simulations over a directed nonlinear dynamical network.

In this article, the evolution of social power is studied within a unified framework comprising two classes of individuals: oblivious individuals and stubborn individuals, whose opinion dynamics are described by the DeGroot averaging model and the Friedkin–Johnsen model, respectively. A proper subset of the simplex is identified to ensure the well-posedness of social power, and it is demonstrated that the corresponding opinion dynamics is convergent for each issue by restricting the initial social power to this proper subset. Through the reflected appraisal mechanism, a nonlinear mapping governing the social power evolution together with its invariant set is derived, and some sufficient conditions with linear time complexity for the convergence of social power are established by proving that this nonlinear mapping is contractive on the invariant set. Furthermore, for the final social power, it is found that both autocratic and democratic social power cannot be achieved during the evolution, and the average social power of oblivious individuals is larger than that of stubborn individuals, indicating that the network topology has a greater impact on social power than individual stubbornness. In addition, it is observed that the final social power ranking of oblivious individuals is consistent with their centrality ranking, and a rigorous lower bound on the final social power is derived for each stubborn individual. Finally, a numerical example is provided to demonstrate the correctness of the theoretical analysis.