<p>This paper focuses on the design of state observers for a wide range of nonlinear systems that are characterized by one-sided Lipschitz and quadratic inner-bounded nonlinearities, which extend the classical Lipschitz framework based on the Lyapunov theory. Unlike traditional Lipschitz conditions, the one-sided Lipschitz property permits a broader and less conservative set of time-varying nonlinear systems. We present sufficient conditions for constructing nonlinear observers that ensure the practical stability of the closed-loop system. Furthermore, we establish a separation principle for nonlinear systems with bounded uncertainties, which aids in the design of observer-based feedback controllers. The theoretical findings are supported by a numerical example that demonstrates the effectiveness and applicability of the proposed approach.</p>