The Boundedness of Nonlinear Control Systems

In this paper we consider nonlinear control sysfemdx/dt=A(t)x+B(t)f(x),(1)Where x(t)∈R~n is the state vector,A(t)=(a_(ij)(t))_(n×n)is the System matrix,B(t),an nxr time-varying matrix,is the input matrix;f(x)∈R~r is nonlinearvector function,and A(t),B(t)∈c[t_0,∞),f(x)∈c[x_0,∞)Here we are to discuss thc boundedness of system(1)in various cases ofmatrix A(t),and the following results shall be obtained.In this paper,weshall use the results of Bihari and other authors.