Stabilization of nonlinear systems by similarity transformations

[摘要] For a systemx˙=A(x)+b(x)u,u(x)=s∗(x)x,x∈ℝn, where the pair(A(x),b(x))is given, we obtain the feedback vectors(x)to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vectorg, a sufficient condition of the existence and an explicit form of a similarity transformationT(A(x),b(x),g)is established. The latter transforms matrixA(x)into the Frobenius matrix, vectorb(x)intog, and an unknown feedback vectors(x)into the first unit vector. The boundaries ofA˜(y,g)are determined by the boundaries of{∂kA(x)∂xk,∂kb(x)∂xk},k=0,n−1¯. The stabilization of the transformed system is subject to the choice of the constant vectorg.

[学科分类] 应用数学