Centralized and decentralized $H_{\infty}$ controller design for storey building systems using matrix inequality approach

Modern control methods have found their way into decentralized design of interconnected systems. Before we find decentralized controller, we first find the centralized controller. Centralized controller will be computed using Linear Matrix Inequality (LMI) approach and decentralized controller will be computed using Bilinear Matrix Inequality (BMI). The BMI will be solved using double LMI via homotopy method which can then be solved efficiently. Numerical example of centralized and decentralized controller of storey building system will be presented. The simulation results on centralized controller show that systems with centralized $H_{\infty}$ controls have better performance than systems without control, and simulation results on decentralized controller show that $\Vert T_{zw}(s)\Vert_{\infty} < \gamma$.