On boundedness of the motions of weakly connected nonlinear systems

Conclusions A general theorem on the boundedness of motions of weakly connected systems is established based on the Lyapunov function method and a comparison principle. Sufficient conditions for uniform boundedness contain the condition of sign-determinacy of a special matrix. A problem on the uniform ultimate-boundedness of motion of a nonlinear system with weak linear bonds is solved as an example.Institute of Mathematics, Academy of Sciences of the Ukraine, Kiev. Kiev University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 29, No. 3, pp. 68–73, March, 1993.