Structured Static Output Feedback Mixed ${H}_2/{H}_\infty $ Control for Linear Control Systems

This note considers the design of static output feedback mixed
${H}_2/{H}_\infty $
controllers for linear control systems with certain equality and inequality constraints imposed directly on the feedback matrix. Based on the barrier method, we solve an auxiliary minimization problem to obtain an approximate solution to the original nonconvex-constrained optimization problem. The necessary conditions for the optimal solution of the auxiliary minimization problem are derived using the Lagrange multiplier method. Subsequently, an iterative steepest descent algorithm is developed to find an approximate optimal solution. Finally, an example is provided to validate the proposed approach.