Optimal guaranteed cost control for linear systems based on state feedback

For the constant linear system and a given quadratic performance index, study the optimal guaranteed cost analysis and control problems based on the linear matrix inequality (LMI) method. Through some lemmas, the conditions of the guaranteed cost state feedback control are converted into a problem of LMI solvability. By solving the LMI, the guaranteed cost controller parameters can be obtained. In turn, give an optimization algorithm with LMI constraints, to obtain optimal guaranteed cost control law. The results can be implemented by the Matlab, and the curve of control and state can be simulated by the Simulink. Finally, two numerical examples are used to verify the feasibility and the correctness of the result.