Abstract
Robust H∞ consensus control problem is investigated for multiagent systems. Each agent is tackled in a more generalized form, which includes parameter uncertainties, external disturbances, nonidentical time-varying state, and input delays. Firstly, a distributed control protocol based on state feedback of neighbors is designed. By a decoupling method, H∞ consensus control problem for multiagent systems is transformed into H∞ control problem for the decoupling subsystems. Then employing Lyapunov-Krasovskii functional and free-weighting matrices, a lower conservative bounded real lemma (BRL) is derived in terms of linear matrix inequalities (LMIs) such that a class of time-delay system is guaranteed to be globally asymptotically stable with the desired H∞ performance index. Extending BRL, a sufficient delay-dependent condition of lower complexity in terms of the matrix inequalities is obtained to make all agents asymptotically reach consensus with the desired H∞ performance index. Furthermore, an algorithm is elaborately designed to get feasible solution to this condition. Extending this algorithm, an optimization algorithm for control protocol parameter is proposed to improve the disturbance attenuation capacity or allowable delay bounds. Finally, simulation results are provided to illustrate the correctness of the theoretical results and the effectiveness of the algorithms.
Highlights
Consensus problem has attracted a great deal of attention due to its enormous potential applications in many areas such as flocking and swarming modeling [1], cooperative control of unmanned air vehicles [2], and formation control of multirobot systems [3]
H∞ consensus control problem for multiagent systems is transformed into H∞ control problem for the decoupling subsystems
A large number of results have been obtained for consensus problem of various multiagent systems, for example, consensus problems of multiagent systems with different dynamics such as doubleintegrator dynamics in [4] and Lipschitz nonlinear dynamics in [5], consensus problems of multiagent systems with the different network topologies such as random networks in [6] and switching topology in [7], and consensus problems of multiagent systems with the different time-delay such as nonuniform time-varying delays in [8] and input and communication delays in [9]
Summary
Consensus problem has attracted a great deal of attention due to its enormous potential applications in many areas such as flocking and swarming modeling [1], cooperative control of unmanned air vehicles [2], and formation control of multirobot systems [3]. Lin et al investigated robust H∞ consensus analysis of directed networks of first-order agents with time-delay and a class of second-order multiagent systems with uncertainty in [10] and [11], respectively. There exists rare work dealing with robust H∞ consensus control problem for uncertain multiagent systems with nonidentical time-varying state and input delays. Motivated by the previous observations, this paper investigates robust H∞ consensus control problem for uncertain multiagent systems, which is subject to parameter uncertainties, external disturbances, and nonidentical time-varying state and input delays. Extending BRL, a sufficient delay-dependent condition in terms of the matrix inequalities, whose complexity is lower because the system is decoupled, is obtained to make all agents asymptotically reach consensus with the desired H∞ performance index. The notation diag{M1, . . . , Mn} denotes a block diagonal matrix whose diagonal blocks are given by M1, . . . , Mn
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