<i>H<sub>∞</sub> </i> Scaled Consensus for MASs With Mixed Time Delays and Disturbances via Observer-Based Output Feedback
Shiming Chen, Zheng Zhang, Yuanshi Zheng
Abstract
In this article, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_{\infty } }$ </tex-math></inline-formula> scaled consensus control problem for multiagent systems in the presence of external disturbances and mixed time delays in both input and Lipschitz nonlinearity is investigated. First, a state observer is introduced for each agent based on the output information of the agent. Then, a scaled consensus protocol is proposed via a truncated predictor output-feedback method, which can deal with the input delay. The integral terms with the mixed time delays that are contained in the transformed systems are analyzed by using the Lyapunov–Krasovskii functionals method, and sufficient conditions are obtained to achieve scaled consensus with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_{\infty } }$ </tex-math></inline-formula> performance. An iterative procedure is utilized to calculate the linear matrix inequality. By this, the feedback gain and observer gain are then designed. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.