A General Stability Test for Switched Positive Systems Based on a Multidimensional System Analysis

The main goal of this technical note is to present a new sufficient condition for the stability of switched positive linear systems. This condition is general in two senses. First of all, because it applies to switching systems of order composed of subsystems, for any and . Secondly, because it applies to both discrete- and continuous-time systems. Furthermore, it is easy to verify, as it amounts to check for the stability of a certain matrix. The new condition is derived from a multidimensional system analysis, where the relation between the stability of multidimensional and switched systems is investigated. A comparison with other existing tests is also presented, showing that the one proposed here allows to infer about the stability of a system in cases where other tests fail or do not apply at all.