Design of optimal linear regulators with steady-state trajectory insensitivity

Optimal linear regulators with steady-state trajectory insensitivity are designed based on a quadratic performance index which includes a time-multiplied quadratic function of the trajectory sensitivity vector. Under the linear feedback control law, the performance index is evaluated by means of the integral transformation. With the aid of the Hamiltonian approach, the optimal feedback control gain, which depends on the solutions of some Lyapunov-type equations, is derived. MATLAB, a computer-aided design package, is employed to implement the optimization algorithm. A numerical example is also given to illustrate the design procedure and to demonstrate the correctness of the proposed method