This paper investigates the distributed quantized $H_{\infty}$ consensus problems for general linear and Lipschitz nonlinear multiagent systems with input quantization mismatch and external disturbances under switching weighted undirected or balanced directed topologies. The designed distributed quantized $H_{\infty}$ consensus protocol can be divided into two parts which are linear and nonlinear parts. The linear part plays a role in achieving satisfactory performance against interval-bounded model uncertainties, external disturbances, and unknown initial states. The nonlinear part eliminates the effect of input quantization. It should be mentioned that complete consensus instead of practical consensus can be achieved in the presence of uniform quantization. In addition, instead of requiring the coupling strength among neighboring agents to be larger than a threshold value as in previous literature, the coupling strength in this paper can be determined by solving some linear matrix inequalities. Sufficient conditions for the existence of the proposed control strategy are also obtained by using the LMI technique. Finally, two numerical examples are presented to show the effectiveness and advantages of the proposed consensus strategy.

Quantized $H_{\infty}$ Consensus of Multiagent Systems With Quantization Mismatch Under Switching Weighted Topologies

This short communication revisits the leaderless consensus problem in directed networks. The network topology is described by a general directed graph which is only needed to contain at least a directed spanning tree, and is not necessarily strongly connected. A bounded and smooth control law using the hyperbolic tangent function is developed as the consensus protocol. Explicit stability analysis based on Lyapunov's second method and the concept of condensation graph is given. The proposed approach transforms the leaderless consensus problem into two subproblems: reaching leader‐following consensus under a graph containing a directed spanning tree with the leader being the root node and reaching leaderless consensus under a strongly connected graph. Remarkably, a perturbed system is formulated as the bridge between these two subproblems which are solved by Lyapunov's second method. The global leaderless consensus is achieved based on the stability of the perturbed system. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed approach.

Reaching global leaderless consensus in directed networks via smooth and bounded control

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

Summary

This paper is concerned with the problem of seeking consensus for a network of agents under a fixed or switching directed communication topology. Each agent is modeled as discrete-time first-order dynamics and interacts with its neighbors via logarithmically quantized information. We assume that the digraph is not necessarily balanced and, thus, avoiding the double stochasticity requirement for the adjacency matrix. For the case of a fixed topology that is strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse logarithmic quantization and the β-asymptotic weighted-average consensus is achieved. For the case of a switching topology that is periodically strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse quantization and the β-asymptotic consensus is achieved. Furthermore, for both cases, not only are the convergence rates for consensus specified but also the bounds on the consensus error that highlight their dependence on the sector bound β of the logarithmic quantizer are also provided. Copyright © 2015 John Wiley & Sons, Ltd.

Reaching consensus in unbalanced networks with coarse information communication

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Reaching consensus in unbalanced networks with coarse information communication