A Feedback Enlargement of Stability Radius Using Non-differentiable Optimization
In controller design of dynamical systems, it is desirable that the controllers can guarantee the stability for not only nominal plants but also perturbed ones, because the plant models may have some uncertainties in their parameters. By this motivation, several researches for the robust controller design have been conducted. In this paper, a feedback controller design method is considered, which achieves enlarging the degree of robust stability for the linear SISO closed-loop systems. Choosing stability radius for the plant parameters as the degree of robust stability, and regarding this as an object function, we formulated this maximization as an optimization problem with constraints coming from prescribed pole placement. The difficulty of this formulation is that while pole placements give linear constraints, the object function is not a smooth one, which calls for an optimization technique for non-differentiable functions. To cope with this, we successfully used the bundle method. We show some numerical examples to illustrate our proposed design method.