Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization
For control theorists working on stochastic hybrid systems, this provides a convex optimization framework for stability tuning, though the result is incremental as it extends existing convexity results to semi-Markov jumps.
The paper addresses stability optimization for positive semi-Markov jump linear systems, showing that tuning system matrix coefficients to maximize exponential decay rate under budget constraints reduces to a convex optimization problem. The approach is validated with a population biology example.
In this paper, we study the problem of optimizing the stability of positive semi-Markov jump linear systems. We specifically consider the problem of tuning the coefficients of the system matrices for maximizing the exponential decay rate of the system under a budget-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 problem reduces to a convex optimization problem 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.