An extended looped‐functional for stability analysis of sampled‐data systems
JunMin Park, PooGyeon Park
Abstract
Summary This article introduces an extended looped‐functional for stability analysis of sampled‐data systems. It is defined as a differentiable functional over an interval between two consecutive sampling instants which has a property that the difference between its values at the latter sampling instant and at the former sampling instant is nonnegative. The proposed looped‐functional includes the existing discontinuous Lyapunov functional and looped‐functional as special cases. Based on the proposed looped‐functional, improved stability criteria are derived in terms of linear matrix inequalities. Three examples show the effectiveness of the proposed criteria in the view of maximum allowable sampling intervals.
Topics & Concepts
Stability (learning theory)Sampling (signal processing)Differentiable functionInstantMathematicsFunctional approachProperty (philosophy)Matrix (chemical analysis)Interval (graph theory)Applied mathematicsComputer scienceMathematical analysisQuantum mechanicsCombinatoricsMaterials scienceFilter (signal processing)Human–computer interactionComputer visionEpistemologyMachine learningPhysicsComposite materialPhilosophyStability and Control of Uncertain SystemsStability and Controllability of Differential EquationsControl and Stability of Dynamical Systems