An improved nonlinear H∞ synthesis for parameter-dependent polynomial nonlinear systems using SOS programming

State feedback control synthesis problems for a class of polynomial nonlinear systems are investigated in this paper. Less conservative sufficient conditions to achieve the closed-loop stability with or without H_infin performance are formulated in terms of state dependent matrix inequalities. By introducing additional matrix variables, we succeed in eliminating the involved coupling between system matrices and the Lyapunov matrix. Hence the proposed methodology can be extended to the synthesis for the parameter-dependent polynomial systems.