Synchronization of discrete-time Lur’e systems under saturating control

This article addresses the problem of control design to ensure the synchronization of discrete-time Lur'e-type systems subject to actuator saturation. Based on a quadratic Lyapunov function and sector conditions, linear matrix in- equalities are derived to ensure that the difference between master and slave states converges asymptoticly to zero in the presence of control saturation. A convex optimization problem is formulated to design an error feedback control law that maximizes the set of admissible initial states. Less conservative conditions are also proposed to address the particular case where the Lur'e-type nonlinearity is described by a piecewise-linear function. Numerical results from a discrete-time chaotic system are considered to illustrate the method.