Robust stability of control systems with polytopical uncertainty: a Nyquist approach

Abstract

For technical plants, a bounded continuum of parameter values describes admissible process models. A robust controller guarantees the observance of minimal requirements for all of the allowed process models. In this paper a frequency domain approach is proposed that permits the instability of a family of polynomials to be checked. This method can be extended in an easy manner to investigate the Instability of a closed loop. The plant is thereby described by a family of models with a polytopical region of uncertainty in the parameter space. As an important special case of the general D-stability, the Hurwitz stability of the closed loop is investigated and a minimal set of necessary and sufficient conditions for robust Hurwitz stability is given. A generalization for other stability domains is possible. Besides an algebraic criterion based on a zero inclusion check for a minimal set of exposed edges of the polytopical region, a graphic criterion of Nyquist type can also be used.