Title: Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers,
Abstract: Linear Parameter-Varying (LPV) systems with jumps and piecewise
differentiable parameters is a class of hybrid LPV systems for which no
tailored stability analysis and stabilization conditions have been obtained so
far. We fill this gap here by proposing an approach relying on the
reformulation of the considered LPV system as an extended equivalent hybrid
system that will incorporate, through a suitable state augmentation,
information on both the dynamics of the state of the system and the considered
class of parameter trajectories. Two stability conditions are established using
a result pertaining on the stability of hybrid systems and shown to naturally
generalize and unify the well-known quadratic and robust stability criteria
together. The obtained conditions being infinite-dimensional semidefinite
programming problems, a relaxation approach based on sum of squares programming
is used in order to obtain tractable finite-dimensional conditions. The
conditions are then losslessly extended to solve two control problems, namely,
the stabilization by continuous and sampled-data gain-scheduled state-feedback
controllers. The approach is finally illustrated on several examples from the
literature.