# IPACS Electronic library

## Bifurcation diagrams of families of regularizable singular systems under proportional and drivative feedback

M. Isabel Garcia-Planas
In this work
we consider differentiable families of triples of matrices $\varphi (\xi)=(E(\xi ),A(\xi ),B(\xi ))$ with the parameter
vector $\xi\in R^{k}$,
representing families of regularizable
singular linear time invariant systems in the form $E(\xi )\dot x(t) =A(\xi)x(t)+B(\xi)u(t)$, with $E(\xi),A(\xi)\in M_{n}( C)$,
$B(\xi)\in M_{n\times m}(C)$ for each $\xi$, under proportional and
derivative feedback.

The knowledge of a complete system of invariants for regularizable
systems permit us to obtain a canonical reduced form and describe
generic families permitting to analyze the neighborhood of a
given system showing bifurcation diagrams of a critical points.