Finite-time H∞ control for one-sided Lipschitz systems with auxiliary matrices

In this paper, finite-time H∞H∞ control is investigated for a class of one-sided Lipschitz systems by using the Finsler׳s lemma. Finite-time boundedness conditions are firstly provided for the one-sided Lipschitz system. The proposed conditions are less conservative since a new Lyapunov function with an additional matrix is constructed, and auxiliary matrices are introduced to make the Lyapunov matrix separate from the system matrix. Then, finite-time H∞H∞ controller is designed by dynamic output feedback. The observer gain and output feedback control gain can be designed in one step optimization. Further discussions and comparisons are also presented in two aspects. At last, numerical simulations are given to verify the validity of the proposed methods.