Stability analysis of positive semi-Markovian jump linear systems with state resets

TL;DR

This paper analyzes the mean stability of positive semi-Markovian jump linear systems, providing a spectral radius-based criterion and a discretization method that preserves stability, with applications to continuous-time systems.

Contribution

It introduces a spectral radius condition for mean stability and a stability-preserving discretization approach for semi-Markovian jump systems.

Findings

Spectral radius characterizes mean stability.

Discretization preserves stability of semi-Markovian systems.

Numerical examples validate the theoretical results.

Abstract

This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continuous-time positive Markovian jump linear systems. Numerical examples are given to illustrate the results.