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In this paper, we study the problem of optimizing the stability of positive semi-Markov jump linear systems. We specifically consider the problems of tuning the coefficients of the system matrices for maximizing the exponential decay rate of the system under a budget-constraint and minimizing the parameter tuning cost under the decay rate constraint. By using a result from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices, we show that the stability optimization problems are reduced to convex optimization problems under certain regularity conditions on the system matrices and the cost function. We illustrate the validity and effectiveness of the proposed results by using an example from the population biology.

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This paper introduces a five-axis active-controlled axial-flux self-bearing motor that uses unipolar and four-pole magnetic fields to control radial force and tilt moment of the two-pole permanent magnet rotor. The proposed method controls the only one-axis radial force and tilt moment by a unit of the rotor and stator, therefore two units are necessary for radial motion control. The stators can be placed on the double-side and single-side of the rotor. In this paper, the principle of the proposed motor is introduced, and the radial force and tilt moment are analyzed theoretically. Then two experimental devices with double-side and single-side stators are made and levitation and rotation tests are carried out. The results confirm that the proposed motor achieved stable rotation up to 900 rpm in a double-side stator and 440 rpm in a single-side stator.