Cloud computing offers the elasticity features by dynamically resizing the infrastructure in response to changes in workload demands to meet performance guarantees and minimize costs. In the last decade, a large body of work has been done in the area of horizontal elasticity, while only few research efforts addressed vertical elasticity. This paper develops a vertical elasticity controller for cloud-based applications using control theory principles to guarantee performance requirements by adjusting the memory allocation as a control knob. The novelty of our work lies on applying a controller synthesis technique by guaranteeing robustness and stability of the controlled system, using the application response time as a decision making criterion. The experimental results reveal that the controller is able to efficiently save at least 47% memory usage while keeping an acceptable user experience.