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A dynamical system is a mathematical model described by a high dimensional ordinary differential equation for a wide variety of real world phenomena, which can be as simple as a clock pendulum or as complex as a chaotic Lorenz system. Stability is an important topic in the studies of the dynamical system. A major challenge is that the analytical solution of a time-varying nonlinear dynamical system is in general not known. Lyapunov's direct method is a classical approach used for many decadesdoi:10.36227/techrxiv.11561361 fatcat:z234h4ydh5b5vnoktsjwrvzp6q