This paper is concerned with both observability and observers for a class of systems described by the two-dimensional hyperbolic PDEs with superlinear boundary conditions which can exhibit chaos. The exact observability and approximate observability are shown by the method of characteristic and boundary reflection relations. Based on the observability, two Luenberger types of PDE observers are designed by making use of the boundary velocity and boundary displacement measurement, respectively. Some sufficient conditions are then developed to obtain the global exponential stability and global asymptotic stability of the observer error systems. Some numerical simulations are performed to validate the theoretical results.  

　　Publication:  

　　SIAM Journal on Control and Optimization, Volume 61, Issue 4 (2023)  

　　https://doi.org/10.1137/21M1462829  

　　Author:  

　　Qiaomin Xiang  

　　School of Mathematics and Big Data, Foshan University, Foshan 528000, China, and Department of Electrical Engineering, Yeungnam University, Kyonsan 38541, South Korea.  

　　Ze-Hao Wu  

　　School of Mathematics and Big Data, Foshan University, Foshan 528000, China.  

　　Ju H. Park  

　　Department of Electrical Engineering, Yeungnam University, Kyonsan 38541, South Korea.  

　　Bao-Zhu Guo  

　　Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, People’s Republic of China.  

　　Email: bzguo@iss.ac.cn