This paper gives a summary of recent work on set-valued systems.On the identification side,for different model structures,different system noises and different set cases,some effective methods such as parameter decoupling,full rank input design,joint identifiability,empirical measure method without truncation and recursive projection identification algorithm are introduced.Based on these methods,the results show that the accurate estimates of the parameters can be achieved even under set-valued information.On the adaptive control side,the asymptotically optimal adaptive control is designed for a class of gain systems with set-valued observations.On the consensus control side,the two-time scale consensus control and the recursive projection consensus control are designed.The multi-agent systems can achieve consensus control by any of the two consensus algorithms.On the application side,we apply set-valued identification methods to complex disease modeling and radar target recognition problems.A new and more effective statistical verification method is constructed.The recognition rate is improved by 10% under low signal-noise ratio.