Synthesis of strongly stable state-derivative controllers for a time-delay system using constrained non-smooth optimization

The paper presents an optimization-based algorithm for stabilizing retarded systems using a state-derivative feedback controller. It is shown that an application of such a controller results in neutral dynamics of the closed-loop system if small feedback delays occur. Therefore, the strong stability theory of neutral systems needs to be considered in the controller synthesis problem. The stabilization approach is based on minimizing the spectral abscissa of the closed-loop system over the controller parameter space, subject to a strong stability constraint. The constrained optimization problem is first turned into an unconstrained problem by application of a barrier method. Subsequently, the optimization is performed using both Broyden-Fletcher-Goldfarb-Shanno (BFGS) and hybrid algorithms for non-smooth optimization Matlab utilities. In the application example, the theoretical results are applied to regenerative chatter suppression in cutting process.