Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

NHC-stabilized dichlorosilaimine ArN＝Si(IiPr)Cl 2 (2) (Ar＝2,6-iPr 2 C 6 H 3 , IiPr＝1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene) and disilane LSiHCl-SiCl 2 L (L＝ArNSiMe 3 ) (3) could be synthesized from the reaction of aminodichlorosilane ArN(SiMe 3 )SiHCl 2 (1) with IiPr under different conditions. This represents the first route to the generation of donor-stabilized dichlorosilaimine from substituted chlorosilane in the presence of an NHC via dehydrosilylation.

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.