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A matrix inequality based design method for consensus problems in multi-agent systems

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Okuno S., Imae J., Kobayashi T.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 4
639-646
EN
In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
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Decentralized design of interconnected $H_∞$ feedback control systems with quantized signals

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Zhai G., Chen N., Gui W.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 2
317-325
EN
In this paper, we consider the design of interconnected $H_∞$ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired $H_∞$ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same $H_∞$ disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.
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