Abstract
In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By estabilshing infinite integrals along solutions of the system and darwing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.
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