First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared respect to accuracy. Then the Hamilton-Jacobi-Belman (HJB) equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it using the Adomian decomposition method is presented.