A Note on Adaptive Observer Design Method for One-Sided Lipschitz Systems

The design problem of adaptive observer for one-sided Lipschitz systems with unknown parameters is addressed. The research focuses on the nonlinear system dynamics which only satisfies one-sided Lipschitz, but not quadratic inner-boundedness. Firstly, an adaptive full-order observer is constructed. Specially, when the one-sided Lipschitz constant is negative, this observer can also be designed. By using the decomposition method, a reduced-order observer is constructed under the same assumptions. The validity of designed observers is illustrated via two examples at last.