Control of Uncertain Systems with l1 and Quadratic Performance Objectives

This thesis presents novel analysis and synthesis concepts for linear control systems with parametric uncertainties. Different performance objectives such as l1, H∞, H2, and quadratic performance are considered. In the analysis section, upper bounds on the l∞-gain (or the l1-norm) of uncertain systems are developed. These bounds exhibit different degrees of computational effort and accuracy. In particular, a new direct approach for determining the robust l∞-gain is proposed. The synthesis sections introduce an efficient formulation of H∞ and H2 constraints in a general linear multi-objective control framework. Moreover, a novel control structure for the design of parameter-varying controllers is developed. Using this structure, a scheme for the synthesis of linear parameter-varying output-feedback controllers in the l1 control framework is presented for the first time. In addition, it is shown how the control structure is applicable to other norm-based frameworks like quadratic performance control and in particular H∞ control. The analysis and synthesis conditions proposed in this thesis are expressed as computationally tractable optimization problems, in particular in form of linear matrix inequalities, semi-definite programs, or iterations thereof. Several detailed examples, including a flight control problem with time-varying dynamics, demonstrate the properties and the applicability of the proposed methods.