Discussion on: 'Global Regulation of Input-Saturated Discrete-Time Linear Systems Subject to Persistent Disturbances'

摘要

Several problems have not been completely solved in the study of linear systems subject to bounded control and affected by external disturbance, i.e., the system described by Eq. (2) in the paper under discussion. One among them is to find conditions on the external disturbances under which an appropriate controller can be designed to achieve external stability with finite-gain. Although the situation is rather involved for unstable plants, for which the domain of attraction is bounded in certain directions, important results can be established for open-loop plants that are marginally unstable (i.e., the eigenvalues of Φ are all inside the closed unit-disk in the discrete-time setting). For a special type of disturbance which affects the system in the form of sat (u(t) + w(t)), the so-called input-additive disturbance, finite-gain external stability results have been established. Since in this case the control signal has the full capacity to counteract the disturbance, finite-gain stabilization is intuitively possible.