Global Stability Analysis with Piecewise Quadratic Lyapunov Functions for Positive Discrete-Time Linear Systems Subject to Saturation in Actuators

This paper introduces an improved approach to characterize the global stability of positive linear discrete-time systems subject to actuator saturation. The ramp function is used to model the saturation function, allowing a precise representation of this nonlinearity. Then, the copositivity of quadratic forms and piecewise quadratic Lyapunov functions depending on both the states and ramps are used to establish sufficient linear matrix inequality (LMI) based conditions for global stability. Numerical comparisons with other techniques from the literature are performed to illustrate the effectiveness of the proposed conditions.