Analysis of the trajectory set of nonlinear dynamics: estimates of solutions and comparison principle
The authors consider families of differential equations of the form \[ D_HX=F(t,X,\alpha),\,\, X(t_0)=X_0\in K_C(\mathbb{R}^n), \] where \(D_HX\) is the Hukuhara derivative, \(F\in C(\mathbb R_+\times K_C(\mathbb R^n)\times S, K_C(\mathbb R^n))\), and \(\alpha\in S\) is a parameter specifying the inaccuracies in the family of differential equations. They obtain estimates for solutions and establish a comparison principle on the basis of an auxiliary matrix-valued Lyapunov function. These results can be used to derive sufficient conditions for the existence properties of trajectories with special properties, including boundedness, practical stability, stability with respect to two measures, structural stability, etc.
scientific article; zbMATH DE number 6136682
scientific article