Abstract
This chapter presents some results which were obtained in recent years, partly by the author in collaboration with others, on the stability and stabilization problem for linear systems on infinite dimensional spaces. Although some of these results are now known to specialists in the control theory, they are not very well known and we hope that this article will make them more available for applications. The chapter coincides with the content of a talk given by the author at the 18-th IFIP TC7 Conference on System Modelling and Optimization. Many problems in physics and engineering can be modelled using equation of zero solution. It is therefore a natural and important problem to generalize the Lyapunov theorem to this infinite dimensional situation.
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