Structural stability of singular systems under proportional and derivative feedback
M. Isabel Garcia-Planas
We consider quadruples of matrices $(E,A,B,C)$,
representing
singular linear time invariant systems in the form $E\dot x(t)
=Ax(t)+Bu(t)$, $y(t)=Cx(t)$ with $E,A\in M_{n}( C)$, $B\in
M_{n\times m}(C)$ and $C\in M_{p\times n}(C)$, under proportional
and derivative feedback, and proportional and derivative output
injection.
In this work study the equivalence relation as a Lie group action
that permit see the equivalence classes as differentiable manifolds
and studying the tangent space to the orbits we obtain a
characterization of the structural stability of quadruples of
matrices, in terms of numerical invariants.