Positive descriptor discrete-time linear systems
Tadeusz KACZOREK
Warsaw University of Technology
Institute of Control and Industrial Electronics
00-662 Warszawa, ul. Koszykowa 75, Gm. E. IIIp.
email: kaczorek@nov.isep.edu.pl
Abstract.
Positive and weakly positive descriptor linear systems are defined. Necessary and sufficient conditions are established under which a weakly positive descriptor system can be transformed by the strict equivalence to a positive system. Some basic properties of the equivalent positive systems are characterised.
Necessary and sufficient conditions are given under which the weakly positive descriptor system can be reduced to a standard positive system. A procedure for computation of matrices of the standard positive system is presented.
Necessary and sufficient condition for the reachablity in n-steps and the observability of the positive systems are also given. It is shown that the weakly positive system may be unreachable in n-steps but it may be reachable in n+1 - steps. An extension of the Cayley-Hamilton theorem for regular pairs is presented.
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