Control of multiterminal HVDC systems embedded in AC networks. Volume 2. Robustness of multivariable control systems

The robustness of the stability of multivariable linear time-invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available and new robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point of a single-input, single-output (SISO) Nyquist diagram. Using the return difference transfer matrix a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness of linear-quadratic-Gaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a cross-feed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linear-quadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.