Internal stabilization of an underactuated linear parabolic system via modal decomposition

Constantinos Kitsos, Emilia Fridman

Research output: Contribution to journalConference articlepeer-review


This work concerns the internal stabilization of underactuated linear systems of m heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the modal decomposition method with a recently introduced state-transformation approach for observation problems, a proportional-type stabilizing control is given explicitly. It is based on a transformation for the ODE system corresponding to the comparatively unstable modes into a target one, where calculation of the stabilization law is independent of the arbitrarily large number of them and it is achieved by solving generalized Sylvester equations recursively. This provides a finite-dimensional counterpart of a recently introduced infinite-dimensional one, which led to Lyapunov stabilization. The present approach answers to the problem of stabilization with actuators not appearing in all the states and when boundary control results do not apply.

Original languageEnglish
Pages (from-to)317-322
Number of pages6
Issue number30
StatePublished - 2022
Event25th IFAC Symposium on Mathematical Theory of Networks and Systems, MTNS 2022 - Bayreuthl, Germany
Duration: 12 Sep 202216 Sep 2022


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