Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls
This paper deals with piecewise-affine (PWA) functions as Lyapunov function candidates for the stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control inputs. Using a PWA model for a saturating closed-loop system, new necessary and sufficient conditions for a PWA function to be a Lyapunov function are presented. Based on a linear programming formulation of these conditions, an effective algorithm is proposed for the construction of such Lyapunov functions and for estimation of the region of local asymptotic stability.
scientific article; zbMATH DE number 1868213