Robust Control Synthesis Examples with Real Parameter Uncertainty using the Popov Criterion

A recent approach to robust control design with real parameter uncertainty has been to use the analysis results from absolute stability theory. Current work has focused on the Popov stability criterion and its extensions because linearized forms of the parameter-dependent Lyapunov functions restrict the allowable time-variations of the parameter errors. This paper builds on recent analysis results, and presents a homotopy synthesis technique for robust controllers that minimise an overbound of an H2 performance objective. The optimal compensator and multiplier are designed simultaneously, which avoids the need to iterate between controller design and optimal multiplier evaluation. The procedure is applied to two and four mass benchmark problems. The results of these examples illustrate the good guaranteed robust performance that can be achieved using this Popov controller synthesis (combined H2/real ¿) algorithm.