A State Observer Design for Dual Lipschitz Nonlinear System

This paper mainly solved the stability of observation error, design of observer and maximization of Lipschitz constant for dual Lipschitz nonlinear system. The sufficient condition for the asymptotic stability of the observation error was obtained by using the Lyapunov method, and the observation gain matrix of the system was acquired by using the way of matrix inequality. According to the observation gain matrix obtained by the design, algorithm solving the maximum allowable upper limit of Lipschitz constant in the state equation and the observation equation was put forward based on the premise of ensuring the stability of the observation error system. The rationality of observer gain matrix is verified by an example, and the maximum allowable limit values of Lipschitz constant under different conditions were given. A simulation was done, and the simulation results show that the algorithm is correct.