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

100%
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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Hybrid stabilization of discrete-time LTI systems with two quantized signals

88%
Zhai G., Matsumoto Y., Chen X., Imae J., Kobayashi T.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 4
509-516
EN
We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.
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