In this thesis, the problem of guaranteed cost control (GCC) for some classes of uncertain nonlinear systems is considered. In particular, the thesis considers two types of problems in this direction: the problem of GCC for uncertain systems subject to actuator saturation and the problem of adaptive GCC for a class of uncertain nonlinear systems which may include systems with hard nonlinearities such as the Coulomb friction. Based on LMI techniques, the thesis proposes new conditions for GCC design, which admit norm-bounded uncertainties and some classes of nonlinearities. The resulting LMI conditions are further used for solving convex optimization problems which minimize the upper-bounds of cost functions associated with the given systems. The solution for the first problem leads to a state-feedback controller that minimizes the upper-bound of the cost function in the presence of uncertainties and actuator saturation. The solution for the second problem leads to an adaptive state-feedback controller that compensates for the effects of uncertain nonlinearities while minimizing the upper-bound of the given cost function. The effectiveness and applicability of the proposed methods is illustrated by using simulation examples, in which an uncertain helicopter model in a vertical plane subject to actuator saturation is considered for the first problem and a 1-DOF mechanical oscillator subject to uncertain Coulomb friction is considered for the second problem.
