The topic of this thesis is H-infinity optimal control of unstable electromechanical system. H-infinity optimization is based on a systematic decrease of H-infinity norm, which represents the highest singular value of transfer function matrix, ie. the highest ratio of the 2-norm of the output signal and the 2-norm of the input signal in terms of signal frequency and in terms of the input signal. H-infinity optimization results with a system with nominally optimal frequency response, but does not necessary have good response in real-life conditions. By introducing the weighting filters, ie. transfer functions used for modification of input and output signals, the original transfer function matrix is being modified for H-infinity optimization purposes with the purpose of penalization of the chosen output signals caused by the chosen input signals. Precise determination of weighting filter results with both good frequency and transient response of the system. In this paper the model of seesaw-cart system is derived. The model of three elastically interconnected seesaw-cart systems is also derived. Derived models are linearised, and linearised models are used for controller synthesis. Investigation of filter parameters influence on specific performance measures of one seesaw-cart model is performed. Obtained results are presented, and can be used as guidelines for future control synthesis. Due to the nonlinear influence of filter parameters on performance measures strict and precise conclusions are impossible, but presented results could be a starting point for future investigations of filter influence on different systems performances. The model of three interconnected seesaw-cart system is used for the investigation of influence of controller's structure on system performance. The centralised controller's structure is modified so it represents set of decentralised or distributed controllers. As expected, the system with centralised control obtains best performance, while performance of the system with distributed control is slightly worse. Possibility of decentralised control with controllers synthesised on one seesaw-cart subsystem while ignoring the rest of system dynamics is considered. System with such control obtained much worse performance. The control of one seesaw-cart system is realised in terms of the computer program and tested on experimental setup developed as part of the project 'Control of spatially distributed dynamical systems'.