Nonsmooth H ∞ Synthesis

We develop nonsmooth optimization techniques to solve H ∞ synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is versatile and can accommodate a number of challenging design problems including static, fixed-order, fixed-structure, decentralized control, design of PID controllers and simultaneous design and stabilization problems. Our algorithmic strategy uses generalized gradients and bundling techniques suited for the H ∞ norm and other nonsmooth performance criteria. We compute descent directions by solving quadratic…