In this article, we pay attention to a Takagi–Sugeno (T–S) system with uncertain disturbance and uncertain measurement noise, in order to accomplish the stabilization of the system relying solely on the bounding information but not on the uncertain disturbance or measurement noise itself. To achieve this objective, an interval observer is designed to estimate the interval bounds of the state of T–S fuzzy systems, and a controller is constructed based on the interval observer. Utilizing the Schur complement, this study establishes sufficient conditions, formulated as linear matrix inequalities, to ensure the efficacy of interval observer-based control for T–S systems. Finally, two simulations are conducted to validate and confirm the accuracy and applicability of the theoretical results.

The distributed state estimation problem of a discrete-time linear time-invariant system is considered in the presence of external disturbances and measurement noise. In this scenario, where only the bounding information of the external disturbance and measurement noise is known, an initial design of a distributed interval observer is implemented to provide a set of intervals within which the state of the system locates, subject to certain requirements on relevant matrices. Subsequently, the Internal Positive Representation technique is introduced to eliminate the aforementioned requirements, so that a distributed observer can be accomplished, with the only prerequisite being collectively detectable of the output measurements of the sensor network. Finally, two examples are proposed to illustrate the effectiveness of the theoretical results.

This article considers the robust consensus problem of the general linear multiagent system (MAS) subject to both heterogeneous additive stable disturbances and input saturation. Distributed low gain feedback-based dynamic output feedback control protocols are proposed, which do not need the controller interaction. Algebraic Riccati equation and unified$H_{\infty }$controller design method are employed to design the output feedback control protocols. It is established that under the assumption that each agent is asymptotically null controllable with bounded controls, semiglobal robust consensus can always be reached under the proposed controller. Furthermore, the design method specialized for leader-following consensus is addressed, under the assumption that the Laplacian matrix is diagonalizable, one can design the control protocol only with the number of follower agents. Finally, several simulations are provided to show the effectiveness of our results.

This work studies the scaled consensus problems of exponentially unstable networked systems with time-varying input delays. First, a distributed consensus algorithm is designed under the truncated predictor feedback technique. Then, a delay bound is evaluated by utilizing the Lyapunov function-based method. Moreover, the consensus can be guaranteed when the upper bound of the time-varying input delay is no more than the delay bound. Furthermore, the relation between the delay bound and the network synchronizability is established. In other words, better network synchronizability implies a bigger delay bound. Finally, in the simulation examples, the feasibility of the theoretical results is verified, and the actual delay bounds are evaluated.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

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.

In this paper, the robust coordination control of multi-agent systems (MASs) with uncertainties is considered, where the uncertainties include the external disturbances and the measurement noises as well as the unknown initial states. Motivated by the interval observer of single-agent systems, a distributed interval observer is designed for MASs communicating through a directed network which contains a directed spanning tree by using only the bounding information on the uncertainties and the output information, to implement the interval-valued state estimation on the absolute state of each agent. It also finds that the robust coordination control is a by-part of the distributed interval observer design of this kind of MASs. Moreover, a time-invariant transformation is used to perfect the distributed interval observer design. Finally, numerical simulations are proposed to verify the theoretical results.

In this article, by using the linear graph theory, modified algebraic Riccati equation (MARE)-based method and duality principle, two interaction protocols are proposed to achieve the scaled edge-consensus of networked discrete-time systems with unmeasurable edge-sates. Meanwhile, drawing support from MARE-based low-gain feedback technique and positive system theory, sufficient conditions are derived to ensure the bounded control inputs and positive edge-states. Moreover, feedback matrices and observer matrices are, respectively, constructed by utilizing the solutions of MARE and modified algebraic dual Riccati equation (MADRE). Remarkably, the theoretical results only use the edge number and vertex number of network rather than the global information of network. Finally, five examples are shown to demonstrate the feasibility of the interaction protocols.

This article investigates the observer-based non-negative scaled edge-consensus problems of a continues-time networked system with or without input saturation, in which the proposed algorithm only uses the neighboring edges’ outputs. First, the original networked model and preliminary algorithm are simplified by using the line graph theory and constructing a new variable. Then the specific mathematical formulations of feedback matrix and observer matrix are both derived by combining$H_{\infty }$control theory and low-gain feedback technique. Next, sufficient conditions which can guarantee the non-negative edge states and bounded control inputs are obtained. Moreover, the advantages of low-gain feedback technique for guaranteeing the non-negative edge states and designing the algorithm are developed. Finally, three cases are used to verify the validity of the theorems.

This article refocuses on the global coordination of networked systems with input saturation and external disturbances. With the help of a novel backstepping approach, a multihop relay control algorithm subject to a group of modified heterogenous saturation functions is constructed, in which the number of the hop is equal to the order of the networked system. It is proved that these modified heterogenous saturation functions can develop a global unsaturated control algorithm for each agent. Then, some sufficient and necessary conditions are provided for the global consensus of the connected networked systems with input saturation in the absence of external disturbances. In the presence of the input saturation and external disturbances, a sufficient condition irrelevant to the interactive network topology information is proposed for the global swarm of connected networked systems. Finally, numerical simulations are provided to verify the theoretical results.

In this article, we take the coordination control problem of linear time-invariant networked systems with uncertain additive disturbance and uncertain initial states into consideration. A distributed interval observer is first constructed for uncertain networked systems in which the control algorithm of each agent involves only the upper bound information and the lower bound information of the interval observer associated with itself and its neighbors, respectively. With the help of the cooperativity theory, it is proved that the interval observer can estimate the piecewise state for each agent and the interval-observer-based control algorithm can drive the uncertain system to achieve coordination behavior. Then, time-varying coordinate transformation is introduced to construct a novel interval observer which can eliminate the cooperativity premise on the system matrices and bound the states of all agents in real time. It is shown that the novel interval-observer-based control algorithm can guide the uncertain system to reach coordinated behavior. Finally, the numerical simulations are provided to verify the theoretical results.

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

This paper addresses the robust semiglobal coordinated control of multiple-input multiple-output multiagent systems with input saturation together with dead zone and input additive disturbance. Observer-based coordinated control protocol is constructed, by combining the parameterized low-and-high-gain feedback technique and the high-gain observer design approach. It is shown that, under some mild assumptions on agents' intrinsic dynamics, the robust semiglobal consensus or robust semiglobal swarm can be approached for undirected connected multiagent systems. Then, specific guidelines on the selection of the low-gain parameter, the high-gain parameter, and the high-gain observer gain have been provided. At last, numerical simulations are presented to illustrate the theoretical results.

Existed works on consensus in networks have been focused on reaching an agreement among states of nodes in a network. In this work, we propose a discrete-time edge consensus protocol for complex networks. By mapping the edge topology into a corresponding line graph, we prove that consensus can be achieved among the states of all edges in a connected network. Theoretical analysis and simulation results are provided to show the effectiveness of the model and the influence of network topology.