Decentralized static output feedback controller design for linear interconnected systems

Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.