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Séminaire du département Automatique du 28/04/2016 à 14h00

 

Analysis and Control of LPV Systems using Hybrid Systems Methods

Intervenant : Corentin Briat, ETH Zurich

Lieu : B208

 

Résumé : LPV systems are often roughly considered to lie within two groups. The  first one contains LPV systems having arbitrarily fast varying  parameters while the second one contains those having continuously  differentiable parameters with bounded derivatives. The first group is most of the time associated with the notion of quadratic stability (common Lyapunov function) whereas the second one with robust stability (parameter dependent Lyapunov function). After a very short review of these ideas, we will consider a particular class of LPV systems with piecewise constant parameters. For such systems, quadratic stability should be considered due to the presence of discontinuities in the trajectories of the parameters. However, by doing so, we would clearly fail in considering the fact that, in between jumps, the parameters are constant.  Note that robust stability cannot be used due to the presence of discontinuities in the trajectories of the parameters. To overcome this, we will rely on the notions of minimum dwell-time and
clock-dependent Lyapunov functions in order to obtain tailored convex stability conditions. These stability conditions are shown to extend and unify the concepts of quadratic and robust stability in a single formulation. The possibility of applying these conditions for stabilization will also be emphasized. These conditions are infinite-dimensional and can be relaxed using, among others, sum-of-squares methods. Finally, if time permits, the extension of these ideas to more general systems, such as LPV systems with piecewise differentiable parameters or with stochastic parameters, will also be informally discussed. 


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