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In this paper, we study the problem of optimizing the stability of positivesemi-Markov jump linear systems. We specifically consider the problem of tuningthe coefficients of the system matrices for maximizing the exponential decayrate of the system under a budget-constraint. By using a result from the matrixtheory on the log-log convexity of the spectral radius of nonnegative matrices,we show that the stability optimization problem reduces to a convexoptimization problem under certain regularity conditions on the system matricesand the cost function. We illustrate the validity and effectiveness of theproposed results by using an example from the population biology.

Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization