More results on the semiglobal stabilization of uncertain nonlinear systems via measurement feedback

We study the problem of semiglobally stabilizing uncertain nonlinear system z˙=Az+Bu+p₁(z, u)u and y=z+p₂(z,u)u, With p_j(z,0)=0, j=1,2, and (A, B) in Brunowski form. We prove that if p₁(z, u)u and p₂(z,u)u are of at least order one and zero, respectively, with respect to the “generalized” dilation δ₁ (z, u)=(l^1-nz₁, ..., l^-1z_n-1 ,z_n, lu), where z_i is the i-th component of z, then we can achieve semiglobal stabilization via arbitrarily bounded measurement feedback