Stability and stabilizability of positive switched discrete-time linear singular systems.

The positivity, stability and stabilizability of switched discrete-time linear singular (SDLS) systems are studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1 and the stability of positive singular systems. We first provide the positive conditions for SDLS systems and the sufficient stability conditions for positive SDLS systems. After that we derive notions and characterizations for stabilizability of positive SDLS systems. Furthermore, we generalize the notion of joint spectral subradius of a finite set of matrix pairs, which allows us to fully characterize stabilizability. [ABSTRACT FROM AUTHOR]