Objective: Tumorigenesis is due to uncontrolled cell division arising from mutations and alterations in the proliferative controls of the cell population. The fight against tumor growth and development has often relied on combination therapy that has been acclaimed as one of the main standards of care in cancer therapeutics and prevention of drug-related resistances. The toxicity of the combinatorial drugs raises a significant concern whenever patients take two or more drugs concurrently at the maximum tolerated dose. A promising solution in tumor treatment involves the administration of the drugs in an alternating or sequential fashion rather than a simultaneous manner. In this paper, we investigate how feasible such an approach is from a mathematical perspective and propose a switched hybrid control systems framework. Methods: We explore the response of tumor cells dynamics to sequential drugs administration with the aid of a time-dependent switching strategy. A transit compartmentalized model is employed to describe the tumor cells progression to death. Results: The design of the time-based drug switching logic ensures the proliferating tumor cells are repressed. Conclusions: Simulation results are provided using the tumor growth dynamics with sequential drugs intake to demonstrate the effectiveness of the proposed method in reducing the tumor size. Significance: This paper is the first attempt to provide a switched hybrid control systems framework on sequential drug administration to biomedical researchers and clinicians.