Stability and angles between state matrices of positive linear systems

Abstract

The stability and the angles between state matrices of positive continuous-time and discrete-time linear systems are addressed. It is shown that: 1) The angles between matrices can be useful tool for analysis of the stability of positive continuous-time and discrete-time linear systems; 2) The positive linear system is asymptotically stable if and only if the symmetrical part of the state matrix is Hurwitz for continuous-time systems and Schur for discrete-time systems; 3) Using the angles between matrices necessary and sufficient conditions are established for the asymptotic stability of the positive linear systemst.