A hybrid optimization approach for discrete-time H∞ static-output-feedback control problem

Optimizing the coordinate transformation matrix is a newly proposed iterative LMI-based approach for solving the H∞ static-output-feedback (SOF) control of discrete-time systems. Once a proper initial coordinate transformation matrix was found, a locally optimal solution for the H∞ SOF control problem can be ensured. However, the problem of how to choose the initial matrix needs to be further studied. This paper applies a cone complementarity linearization (CCL) strategy to solve this problem. Then, a hybrid optimization approach is developed to solve the H∞ SOF control problem. Finally, numerical examples are provided to demonstrate the effectiveness and advantages of the proposed method.