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

TL;DR

This paper presents a convex optimization approach to enhance the stability of positive semi-Markov jump linear systems by tuning system matrices, with applications demonstrated in population biology.

Contribution

It introduces a novel convex optimization framework for stability tuning of semi-Markov jump systems using spectral radius properties.

Findings

The stability optimization problem is reducible to a convex form.

The approach is validated with an example from population biology.

The method effectively maximizes the exponential decay rate under constraints.

Abstract

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.