In control theory the main issue is to find controllers, such that a given system can be regulated into a desirable behaviour. In this thesis we have formulated some control problems using LMIs, and we have developed some conditions under which a controller with some desired properties exists.
Controllers can be of different complexity, measured by the order of the controller.
The algorithm is guaranteed to converge to a stationary point and extensive numerical results show that the algorithm in many cases finds optimal solutions. Based on the balancing algorithm we have developed a new algorithm, which, by numerical experiments, seem to improve the results of the balancing algorithm. We have also compared the algorithms to alternative algorithms. The numerical experiments show that our algorithms work very satisfactorily. Last updated June 19, 2001.