Stability analysis of LPV systems with piecewise differentiable parameters
For control theorists working on LPV systems, this fills a gap by providing stability conditions for a previously unaddressed parameter class.
The paper addresses stability analysis for LPV systems with piecewise differentiable parameters, for which no proper conditions existed. It proposes a hybrid systems reformulation that yields stability conditions generalizing quadratic and robust criteria, demonstrated on two examples.
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of hybrid systems. The underlying idea is to reformulate the considered LPV system as an 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. Then, using a result pertaining on the stability of hybrid systems, two stability conditions are established and shown to naturally generalize and unify the well-known quadratic and robust stability criteria together. The obtained conditions being infinite-dimensional, a relaxation approach based on sum of squares programming is used in order to obtain tractable finite-dimensional conditions. The approach is finally illustrated on two examples from the literature.