On the asymptotic stability and instability of the zeroth solution of a non-autonomous system
The system \(x'=X(t,x)\) is considered in n-dimensional space where X is measurable in t for fixed x, continuous in x for fixed t and satisfies certain generalized boundedness and Lipschitz conditions such that the bound and the ''Lipschitz constant'' are functions of t satisfying some requirements. The existence of limiting equations is assumed and limiting functions of some Lyapunov functions are defined. Several stability theorems are proved under some conditions imposed upon the limiting equations and limiting Lyapunov functions. The results are applied to the motion of a solid of variable mass in a resistive medium, to the Lagrange equations of a mechanical system with time dependent constraints, and to the problem of synthetization of the control moment assuring the asymptotic stability of a given triaxial orientation of a solid with variable moments of inertia.
scientific article; zbMATH DE number 3936565
scientific article