In the last two decades wind energy industry has been developing rapidly which implies growth of the installed wind power, as well as an increase in wind turbine dimensions. This brings up the question of optimizing wind turbine operation, as small increase in energy conversion efficiency and/or extension of wind turbine lifetime would result in a considerable increase in profitability. One of the approaches to achieve these goals is to improve the wind turbine control system. There has been a lot of research activity in this area and application of various advanced control methods to wind turbines can be found in the literature. Application of these advanced control methods to wind turbines has two main goals: (i) increase in energy conversion efficiency, (ii) reduction of wind turbine structural loads. In this thesis H_infinity control and Linear Parameter Varying (LPV) control are investigated with the aim to achieve: goal (i) by improving wind turbine rotational speed control (thus improving produced power quality and reducing risk of shut down due to occured overspeed), and goal (ii) by reducing tower vibrations (thus extending wind turbine lifetime). The thesis considers control of a modern, large wind turbine (rated power of 1 MW and above) which has three-bladed rotor turned towards the wind (upwind machine) and horizontal shaft with generator placed in the nacelle on the top of the tower. Considered wind turbine has direct drive (without gearbox) and a synchronous generator which is connected to the grid over an AC-DC-AC converter which allows generator speed to be varied in a wide range. Such wind turbines are controlled by adjusting the generator torque (below rated wind speed) and by pitching the turbine blades (above rated wind speed). Classical wind turbine control system is described in detail and it is validated by computer simulations. All the simulations presented in the thesis are carried out in professional software tool GH Bladed which uses detailed mathematical model based on the modelling method called Blade Element and Momentum Theory (BEM). Since this complex model is not appropriate for the control system design (mainly due to implicit relations that it uses), simplified mathematical model is used for synhtesis of both classical and advanced wind turbine controllers. Wind turbine system is very nonlinear and electrical energy production is dominantly dependent on the stochastical disturbance - the wind. Therefore, it is important to ensure that the wind turbine control system is robust with respect to disturbance and system nonlinearity. Furthermore, in order to achieve opposing objectives in wind turbine control (increase in efficiency and reduction of loads) some kind of multicriterial algorithm must be used, i.e. multivariable controller which makes use of multiple process variable measurements (or estimations). H_infinity and LPV are known as methods for designing multivariable, robust controllers which makes them appropriate for the application to wind turbines. H_infinity control theory is used for the design of linear time-invariant, robust, multivariable controllers which ensure stability and the desired performance of the closed-loop system. There are two basic approaches to H_infinity controller synthesis: older, classical one which uses Riccati equations and newer one which uses linear matrix inequalities. Both approaches are described and exploited in the thesis. Due to wind turbine system nonlinearity, linear time-invariant H_infinity controllers are not sufficient for quality control in real conditions where wind speed varies significantly. Therefore, some adaptive control strategy must be adopted. In this context, the most logical choice is LPV control which can be regarded as the extension of H_infinity control to nonlinear and/or time-varying systems. LPV controllers can guarantee stability and the desired performance of the nonlinear closed-loop system, because variation of the working conditions can be taken into account. The thesis investigates H_infinity and LPV control theories and possibilites of their application to wind turbines. Among other things, the following topics are researched and explained: introduction and basic idea of H_infinity control theory, weighted sensitivity and mixed sensitivtiy problems, weighting functions and guidelines for choosing them, two approaches to H_infinity controller synthesis (along with their characteristics and implementation in available software packages), LPV control theory (along with its application to nonlinear systems and links to H_infinity control theory). New control system is developed only for the operating region above rated wind speed where forces and loads are higher and it is expected that the improvements can be achieved in this region. This is supported by the fact that the H_infinity method is used for shaping frequency responses of the closed loop system which are closely related to structural oscillations. Wind causes thrust force on the rotor which is the main excitation for tower nodding in the fore-aft direction (direction of the wind). These vibrations are one of the main contributors to wind turbine structural loads and they represent the biggest limitation for classical pitch controller design. This is the case because thrust force on the rotor depends on the pitch control strategy to a large degree. Inadequate pitch control can lead to large tower vibrations and wreckage of the turbine construction. On the other hand, smart pitch control can reduce tower nodding. Tower vibrations must be considered for larger, as well as for smaller wind turbines. Therefore, the emphasis in the thesis is put on tower vibration attenuation. Literature which deals with application of H_infinity and LPV methods to wind turbines does not systematically approach to imposing requests on the control system behaviour by parametrization of the weighting functions which is a key step in H_infinity and LPV controller synthesis. Furthermore, in the available literature it is not shown how to enforce the LPV controller to hold the operating point without adding additional control loops, the interaction of which with the LPV controller is hard to validate theoretically. These shortcomings are addressed in the thesis. Application of H_infinity control theory to large wind turbines (in a single operating point defined by the wind speed) is investigated by the following steps: (i) problem formulation, in terms of choosing model structure for controller synthesis, (ii) weighting function structure and parameter selection, (iii) optimization problem formulation and its particularities, (iv) practical details regarding implementation. Application of LPV control theory to large wind turbines (in the whole operating region above rated wind speed) is investigated in a way that the procedure (described by the steps given above) is systematically extended and applied to multiple operating points above rated wind speed. Proposed algorithms and methods are validated in order to obtain plausible insight on the implications of their application to real, large wind turbines. Validation is performed: (i) by using computer simulations - in GH Bladed, (ii) experimentally - on real, laboratory wind turbine (situated at Faculty of Electrical Engineering and Computing, University of Zagreb) which emulates large wind turbines. Simulation results are thoroughly analyzed in time and frequency domain, while control impact on wind turbine structural loads is evaluated via Damage Equivalent Loads (DEL) calculation. In this thesis DELs are calculated on the basis of load time traces obtained from GH Bladed simulations.