Adaptive state observer for Lipschitz nonlinear systems

The problem of adaptive observer synthesis for Lipschitz nonlinear systems is addressed. In the case of known parameters, the convergence property of state observer is first discussed. Based on a generalized Lipschitz condition, the sufficient conditions to ensure the stability of observer error dynamics are presented in terms of some LMIs. In the case of system dynamics with some unknown parameters, the proposed conditions along with an equality constraint are then employed to guarantee the convergence property of an adaptive state observer. Moreover, an adaptive observer form is derived which can be utilized in designing the reduced order state observer. The simulation results are finally given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems.