Decentralized control of discrete-time linear time invariant systems with input saturation

We study decentralized stabilization of discrete-time linear time invariant (LTI) systems subject to actuator saturation, using LTI controllers. The requirement of stabilization under both saturation constraints and decentralization impose obvious necessary conditions on the open-loop plant, namely that its eigenvalues are in the closed unit disk and further that the eigenvalues on the unit circle are not decentralized fixed modes. The key contribution of this work is to provide a broad sufficient condition for decentralized stabilization under saturation. Specifically, we show through an iterative argument that stabilization is possible whenever 1) the open-loop eigenvalues are in the closed unit disk, 2) the eigenvalues on the unit circle are not decentralized fixed modes, and 3) these eigenvalues on the unit circle have algebraic multiplicity 1.