Computer Algebra Algorithms for Control Related Tests of Implicit Dynamic Systems

This contribution is focused on control related tests for implicit dynamic systems, like accessibility, observability or input to output, input to state linearizability. Since the performance of these tests needs tedious symbolic calculations, computer algebra systems are the ideal tool to cope with this problem. Accessibility and observability are exemplarily used to present a new approach based on Lie groups. It is shown that non accessible or non observable systems admit Lie-groups acting on their solutions such that dinstinguished parts remain unchanged. This fact allows us to apply this technique, as well as its realization by computer algebra algorithm, to several fundamental problems in control.