On partial asymptotic stability by the method of limiting equation
The well-known Barbashin-Krasovskij theorem, which establishes asymptotic stability for the zero solution of a differential system by a Lyapunov function with a negative semi-definite derivative (with respect to the given system), is extended to the partial asymptotic stability in the sense of V. V. Rumyantsev. Contrary to the previous extensions by \textit{V. V. Rumyantsev} [Sympos. Math. 6, 243-265 (1971; Zbl 0226.34047)], \textit{A. S. Oziraner} [Prikl. Mat. Mekh. 37, 659-665 (1973; Zbl 0295.34046)] and \textit{C. Risito} [Ann. Mat. Pura Appl., IV. Ser. 84, 279-292 (1970; Zbl 0213.106)], the condition of the boundedness of the uncontrolled coordinates is replaced by that not requiring ''a priori'' knowledge of the solution. Moreover, some applications to the stability properties of the equilibrium of dissipative nonholonomic mechanical systems are given.
dissipative nonholonomic mechanical systems
scientific article; zbMATH DE number 3910818
scientific article