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）∈Rn is the state vector,A（t）=(aij（t）)n×nis the System matrix,B（t）,an nxr time-varying matrix,is the input matrix;f（x）∈Rr is nonlinearvector function,and A（t）,B（t）∈c[t0,∞),f（x）∈c[x0,∞)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.