New Haar-Based Algorithms for Stability Analysis of LPV Systems

New gridding-based algorithms for stability analysis of linear parameter-varying systems with general parameter dependencies are introduced. Recent results in Haar-based Lyapunov stability analysis allow to treat non-convex parametric domains and a large class of system parameter functions by using computationally implementable algorithms to solve the original infinite-dimensional and infinitely constrained problems, without requiring further checks even for arbitrarily sparse parameter grids. In contrast with previous theoretical results which are not constructive from the algorithmic and numerical point of view, the approach introduced here is systematic and amenable for practical implementation, avoiding complex analytical manipulations when a vast class of parameter dependencies is considered. Two numerical examples are used to validate the proposed algorithms.