Flux estimation is essential in most advanced control schemes of induction machines like indirect field‐orientation control and feedback linearizing approach. In this paper, optimal control theory and Lyapunov stability analysis are applied to design the full‐order flux observer of induction machines. The observer refers only to measurable quantities which are composed of terminal voltages, currents and rotor speed. The time‐invariant and time‐varying portions of the error dynamics of the observer are minimized separately. The degree of relative stability of the observer can be prescribed at the beginning of the design and is independent of speed variations. In the presence of uncertainty in rotor resistance, a sufficient condition for the design with bounded estimation errors is derived and the resultant residual can be formulated explicitly. Results from computer simulations show that the method exhibits excellent convergent characteristics and robustness to rotor resistance uncertainty.