This paper is concerned with piecewise-linear functions as Lyapunov function candidates for stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control inputs. New necessary and sufficient conditions for positive definite piecewise-linear functions be Lyapunov functions are presented. A computational procedure is proposed for determination of such Lyapunov functions and associated polyhedral regions of local asymptotic stability. Compared to Minkowski functions, piecewise-linear functions present strictly better performance, being naturally more flexible and better adapted to the radially variable dynamic behavior of saturated systems.
Discrete-time systems; saturation; stability; Lyapunov functions; piecewise-linear functions; linear programming
