A review on benchmarks Examples for dynamical hybrid systems controller synthesis to facilitate its selection process

Due to various and complex phenomena in hybrid dynamical systems, the control of these types of systems has faced a challenge. Space systems also have hybrid dynamics due to different missions and operational modes. Therefore, to deal with these systems, we must first familiarize ourselves with the standard examples studied before. Consequently, multiple examples have been reviewed and researched in hybrid control science. Some of these examples are used as benchmarks to improve the performance comparison of control methods or to check their comprehensiveness. Therefore, this article has tried to collect benchmark examples with different characteristics in the hybrid control field and compare them with each other. It should be noted that benchmark examples were selected based on the number of repetitions and being well recognized. Therefore, the performance of the developing controllers can be examined on these examples and compared with the results of other controllers. As a result, the researchers can choose their desired benchmark more accurately and efficiently and proceed with the investigation and design of the controller.