Abstrakt
The concept of inverse systems for standard and positive linear systems
is introduced. Necessary and sufficient conditions for the existence of
the positive inverse system for continuous-time and discrete-time linear
systems are established. It is shown that: 1) The inverse system of
continuous-time linear system is asymptotically stable if and only if the
standard system is asymptotically stable. 2) The inverse system of
discrete-time linear system is asymptotically stable if and only if the
standard system is unstable. 3) The inverse system of continuous-time and
discrete-time linear systems are reachable if and only if the standard
systems are reachable. The considerations are illustrated by numerical
examples.
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