Abstract Stability analysis and design for continuous-time proportional plus derivative state observers is presented in the paper with the goal to establish the system state and actuator fault estimation. Design problem accounts a descriptor principle formulation for non-descriptor systems, guaranteing asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess parameter existence of the proposed estimator structure. The obtained design conditions are verified by simulation using a numerical illustrative example.