Decentralized Observer-based Controller Design for Linear Interconnected Systems

Many natural processes are shown as interconnected systems. Therefore, the decentralized controller is proposed to eliminate a loss that can cause all systems to fail. In most practical cases, some system states are unmeasurable, so an observer to estimate the state value is considered. Since the observer-based decentralized controller is represented as Bilinear Matrix Inequality (BMI), we use an efficient method to compute a feasible solution for BMI. A Homotopy method solves BMI by fixing unknown variables such that the inequality matrix can be solved by Linear Matrix Inequality (LMI). We present a numerical example to validate the proposed method.