Simultaneous stabilization of a segment of systems by a parameterized compensator

An interpolation approach with stable polynomial interpolants applied to the simultaneous stabilization of a segment of systems

“…For that, consider the closed loop system G λ with the controller C defined in (1) and study the characteristic polynomial Φ(G λ , C) given by (4) …”

“…By considering the approach described in [4] which is inspired of [3] and adapted to the case of the simultaneous stabilization of a segment of systems, then this control problem is formulated as a BMI and approximated as a rank-one LMI optimization constraint. Unfortunately, if we apply this method to this example, we have to manage a computational complexity that does not allow to process and to look for solutions.…”

“…In this context, [3] gives bilinear matrix inequality (BMI) conditions for stabilizing simultaneously a finite family of n systems when the order of the controller is fixed. That is this method that we have initially adopted to deal with the case of the simultaneous stabilization of a segment of systems, see [4]. Unfortunately, there does not exist off-the-shelf algorithms for solving this non-convex problem formulated as BMIs.…”