The Method of Exponential Differential Inequality in the Estimation of Solutions of Nonlinear Systems in the Vicinity of the Zero of the State Space

摘要

We consider a system of differential equations in the Cauchy form, containing homogeneous linear and cubic forms with respect to phase variables and small perturbing functions. We consider the system as a polynomial dynamical system under constant disturbances. We propose a method for constructing a nonlinear exponential differential inequality for a quadratic Lyapunov function and a square inequality. By integrating the exponential differential inequality, we obtain an estimate of the Lyapunov function from a function of time and initial conditions and an estimate of the phase variables.