Asymptotic and L2 stability analysis for a class of nonlinear discrete-time control systems subject to actuator saturation

This paper addresses the stability characterization problem for a class of nonlinear discrete-time control systems subject to actuator saturation and energy bounded disturbance inputs. The considered class of systems covers all nonlinear discrete-time systems that can be modeled by rational difference equations. The results are based on a recursive algebraic representation of the nonlinear control system and a generalized sector bound condition to deal with the saturation effect. From these elements, LMI based conditions are proposed to analyze the asymptotic stability and both the L₂ input-to-state and input-to-output stability properties. The proposed conditions are then incorporated into convex optimization problems to either maximize an ellipsoidal estimate of the region of attraction or a bound on the admissible L₂ disturbances, and also to minimize a bound on the system L₂-gain.