# Optimal stabilization of bodies in electromagnetic suspensions without measurements of their location

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## Abstract

The optimal stabilization problem is considered for bodies in electromagnetic suspensions. To solve this problem, we form a linear stationary control law for the linearized system. This law is based on the feedback principle and uses the measuring of the current intensity in the circuit of the electromagnet, while the location of the body and its velocity are not measured. The optimality criterion is the generalized *H* _{∞}-norm of the linearized system: it characterizes the extinguishing level for perturbations generated by external actions and unknown initial conditions. To compute the feedback parameters, the technique of linear matrix inequalities is applied. We provide mathematical simulation examples for the dynamics of a body in an electromagnetic suspension.

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