This talk will introduce how chain scattering-matrix descriptions and coprime factorizations, can be employed to develop a unified method for solving a fairly general class of control synthesis problems. It will be shown that the control synthesis problem can be represented in terms of two associated chain scattering-matrix descriptions, and then solved via two coprime factorizations. The approach is first developed in terms of the transfer function matrices, which promotes a good understanding of how to solve the control problem, and then the corresponding formulae are given in state-space form, to show how the solution is calculated.
As a tutorial in using this approach, examples will be given to show how to characterize all stabilizing controllers, H-infinity controllers and H-2 controllers via the associated coprime factorizations (for example with a J-lossless numerator as required for H-infinity control). Connections between the fundamental full information and full control problems and the general H-infinity problem will be also given. Finally some properties of the well-known H-infinity loop shaping design will be addressed. The presented materials have, in fact, been developed during my stay in Cambridge so I would like to share them with everyone in the control group.
Back to Control Seminars Page