Computing Continuous Time-Varying Matrices’ Generalized Eigenvalues Using ZD (Zhang Dynamics) Method

Generalized eigenvalue plays an important role in science and engineering fields. The problems of static generalized eigenvalue have been studied for many years. Different from the researches of static matrix problems, in this paper, the problem of solving generalized eigenvalues of time-varying matrix is studied. Zhang dynamics (ZD) is a convenient and effective method with powerful capabilities to solve time-varying problems. With the help of ZD method, two error functions are designed, and a continuous-time model, which is described in the form of a differential equation, is obtained. Furthermore, the generalized eigenvalues of two typical examples are solved. Numerical results not only verify the validity and convergence of the continuous-time model, but also substantiate the effectiveness of ZD method in solving time-varying matrix problems.