Closed-loop perturbations of well-posed linear systems

We are concerned with the perturbation of a rather general class of linear time-invariant systems, namely well-posed linear system (WPLS), under additive linear perturbations seen as feedback laws. Let \(\Sigma\) be a WPLS with \((A, B, C)\) as generating triple. For all control operator \(E\), and all observation operator \(F\) such that \((A, E, F)\) is the generating triple of a WPLS, we prove that, if \((A, B, F)\) and \((A, E, C)\) are also the generating triples of some WPLS, for all admissible feedback operator \(K\) for \((A, E, F)\), we can construct a WPLS \(\Sigma^K\) whose generating triple is \((A^K, B^K, C^K)\), where \(A^K\) is the infinitisemal generator of the closed-loop of \((A, E, F)\) by the feedback operator \(K\). Furthermore, we give necessary and sufficient condition such that exact controllability persists from \(\Sigma\) to \(\Sigma^K\). In particular, we show that this is the case for all sufficiently small bounded operator \(K\).

To cite this paper:
Haine Ghislain (2017) Closed-loop perturbations of well-posed linear systems. IFAC-PapersOnLine 50(1):4546–4551. Toulouse, France.

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