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Existing active magnetic bearings (AMBs) operate in the linear region of the magnetic material flux density,which limits the utilization of the bearing capacity.In order to increase the utilization of the bearing capacity and enhance the performance of the AMB system,this paper develops a method for designing high performance linear feedback laws.The resulting feedback laws allow the AMB to operate in its nonlinear region and hence improve the closed-loop performance.We first establish an approximate nonlinear AMB current force response model,and place this nonlinear curve inside a sector formed by two piecewise linear lines.Based on the linear line segments in these two piecewise linear lines,we determine the maximum disturbance that can be tolerated by solving an optimization problem with linear matrix inequality (LMI) constraints.For a given level of disturbance under the maximum tolerable disturbance,we formulate and solve the problem of designing the linear feedback that achieves the highest level of disturbance rejection as another LMI problem.Both L2 disturbances and L∞ disturbances are considered.Finally,we illustrate our design by both simulation and experimental results.