Decentralised controller design for a large-scale linear discrete-time polytopic uncertain systems

One of the great challenges to control theory is to design controllers for the increasing size of uncertain large-scale systems. Such problems arise in many real-word applications and the systems are too large and too complex to be centralised controlled. For these reasons, the complex system is split into several interconnected subsystems and it is controlled in a decentralized fashion. In this article, a novel, original approach to the control of large-scale uncertain linear discrete-time systems by a decentralised controller is presented. In the existing references, such systems are divided into two groups: complex systems with strong or weak interactions. However, the new proposed approach depends on whether the system is stable or not. The design procedure consists of two steps: In the first step, the dynamic properties of the closed-loop decentralised controlled subsystems are determined in such a way that the stability, robustness, and performance of the closed-loop subsystems and the entire system are guaranteed. In the second step, a decentralised control algorithm must be designed that ensures the required properties of the subsystems that have been obtained in the first step. The advantage of this approach is that the decentralized controller design is performed on the subsystem level.