On the diagonal stability of a class of almost positive switched systems

Necessary and sufficient conditions are derived in this paper for the existence of a diagonal Lyapunov function for a class of switched systems. The switching is carried out intermittently between the open loop and the closed loop of a feedback system, a procedure encountered frequently in many interconnected systems at the present time. The open loop system considered in the paper is described by a stable Metzler matrix, which is known to be diagonally stable. The closed loop system is stable, but does not retain the Metzler property. The existence of a common diagonal Lyapunov function assures system stability for arbitrary switching. This decouples stability and performance issues in the switched system, and permits switching to be carried out entirely for improving performance. Towards the end of the paper, it is also shown that some recent results in the control literature can be derived as special cases of the principal results derived in the paper.