A Nonsmooth Optimization Approach to H ∞ Synthesis

A numerical method for solving the H∞ synthesis problem is presented. The problem is posed as an unconstrained, nonsmooth, nonconvex minimization problem. The optimization variables consist solely of the entries of the output feedback matrix. No additional variables, such as Lyapunov variables, need to be introduced. The optimization procedure uses a line search mechanism where the descent direction is defined by a recently introduced dynamical systems approach. Numerical results for various benchmark problems are included.