Designing a Set of Stabilizing Controllers Using D-Decomposition for the System Described by a Generalized Bode Envelope

Designing stabilizing controllers that could achieve not only stability but also desired performance characteristics for an uncertain family of plants is highly important for control applications. We propose a novel approach based on the classical D-decomposition technique that allows designing a range of controller parameters such that required performance is achieved and by that allows flexibility in choosing a robust controller. We describe a family of plants by non-parametric generalized Bode envelopes. Our examples demonstrate how the proposed technique is applied with and without uncertainties in the plant model. While the treatment is provided for linear time-invariant uncertain systems, similar approaches could be developed for systems with delays and nonlinear systems with uncertainties.