Stability analysis of positive linear systems by decomposition of the state matrices into symmetrical and antisymmetrical parts

摘要

The stability of positive linear continuous-time and discrete-time systems is analyzed by the use of the decomposition of the state matrices into symmetrical and antisymmetrical parts.It is shown that:1)The state Metzler matrix of positive continuous-time linear system is Hurwitz if and only if its symmetrical part is Hurwitz;2) The state matrix of positive linear discrete-time system is Schur if and only if its symmetrical part is Hurwitz.These results are extended to inverse matrices of the state matrices of the positive linear systems.