Robust disturbance rejection by the attractive ellipsoid method – part II: discrete-time systems

This paper presents sufficient conditions for the robust stabilization of discrete-time polytopic systems subject to control constraints and unknown but bounded perturbations. The attractive ellipsoid method (AEM) is extended and applied to cope with this problem. To tackle the stabilization problem, new linear matrix inequality (LMI) conditions for robust state-feedback control are developed. These conditions ensure the convergence of state trajectories of the system to a minimal size ellipsoidal set despite the presence of non-vanishing disturbances. The developed LMI conditions for the AEM are extended to deal with the problem of gain-scheduled state-feedback control, where the scheduling parameters governing the time-variant dynamical system are unknown in advance but can be measured in real-time. A feature of the obtained conditions is that the state-space matrices and Lyapunov matrix are separated. The desired robust control laws are obtained by convex optimization. Numerical simulations are given to illustrate the feasibility of the proposed AEM for robust disturbance rejection