The lucrative features of cloud computing such as pay-as-you-go pricing model and dynamic resource provisioning (elasticity) attract clients to host their applications over the cloud to save up-front capital expenditure and to reduce the operational cost of the system. However, the efficient management of hired computational resources is a challenging task. Over the last decade, researchers and practitioners made use of various techniques to propose new methods to address cloud elasticity. Amongst many such techniques, control theory emerges as one of the popular methods to implement elasticity. A plethora of research has been undertaken on cloud elasticity including several review papers that summarise various aspects of elasticity. However, the scope of the existing review articles is broad and focused mostly on the high-level view of the overall research works rather than on the specific details of a particular implementation technique. While considering the importance, suitability and abundance of control theoretical approaches, this paper is a step forward towards a stand-alone review of control theoretic aspects of cloud elasticity. This paper provides a detailed taxonomy comprising of relevant attributes defining the following two perspectives, i.e., control-theory as an implementation technique as well as cloud elasticity as a target application domain. We carry out an exhaustive review of the literature by classifying the existing elasticity solutions using the attributes of control theoretic perspective. The summarized results are further presented by clustering them with respect to the type of control solutions, thus helping in comparison of the related control solutions. In last, a discussion summarizing the pros and cons of each type of control solutions are presented. This discussion is followed by the detail description of various open research challenges in the field.