This paper proposes a convex optimization approach for the design of robust observers applied to the control of five phase induction machines subject to rotor resistance variation and load disturbance. Based on the first and third harmonic dynamic models of the multi-phase machine, two robust observers are proposed to estimate the rotor flux components. The two observers are applied to the direct field oriented control of a five phase induction machine, where simulation results have demonstrated a high dynamic performance and robustness to parametric variations of the proposed setup.