Extension of zakian’s theory of majorants to two-input two-output feedback systems

Abstract

The main aim of the thesis is to extend the theory of majorants, which was developed previously for the case of single-input single-output feedback systems, to the case of two-input two-output systems. The theory of majorants provides useful inequalities for designing feedback systems in which the plant model is described by non-rational transfer functions or in which the plant model has uncertainties. For the design formulation considered in this work, the design objective is to ensure that the errors and the controller outputs always stay within prescribed bounds whenever the possible inputs satisfy certain bounding conditions on magnitude and slope. The thesis consists of two main parts. Part 1 extends the criterion of approximation for single-input single-output feedback systems to the case of two-input two-output systems, and later to multi-input multi-output systems, where nonrational transfer matrices are replaced with rational approximants during the design process. In part 2, based on the developed criterion, inequalities for designing two-input two-output vague systems are derived and investigated. Numerical examples are given in order to illustrate the effectiveness and the usefulness of the methods developed here.