Algebraic theory of linear multivariable control systems

Abstract

The theory of linear multivariable systems stands out as tlie most developed and sophisticated among the topics of system theory. In the literature, many different solutions are presented to the linear midtivariable control problems using three main approaches : geometric approacli, fractional approach and polynomial model based approach. This thesis is a first draft for a textbook on linear multivariable control which contains a description of solutions to the most of the standard algebraic feedback control problems using simple linear algebra and a minimal amount of polynomial algebra. These problems are internal stabilization, disturbance decoupling by state feedback and measurement feedback, output stabilization, tracking with regulation in a scalar system, regulator problem with a single output channel and decentralized stabilization.