Asymptotic stability of large scale dynamical systems using computer generated Lyapunov functions
The stability of equilibrium points of large scale dynamical systems described by differential equations of the form x = f(x) is analyzed using computer generated Lyapunov functions;Recently, Brayton and Tong developed a constructive algorithm for use in the stability analysis of dynamical systems; however, their method of analysis taxes the capabilities of most modern computers when applied to high dimensional systems. To circumvent these difficulties, we divide an interconnected system into lower order subsystems. Lyapunov functions of the isolated subsystems are constructed using Brayton and Tong's constructive algorithm. An aggregated text matrix for the stability analysis of the entire system is determined in terms of the qualitative properties of the isolated subsystems and in terms of the interconnecting structures of the entire system. If this matrix is an M-matrix, then the system is guaranteed to be asymptotically stable in some region;The above results are applied to a multimachine power system to estimate the stability region of the overall system, and to estimate the critical clearing time if the power system is faulted during its steady state operation. The results are also applied in stabilizing a long train control system so that the system is globally asymptotically stable.