This paper investigates the input/output constrained control for the
planar vertical/short takeoff and landing aircraft. The controller construction is based on a descriptor system formulation. The resulting nonlinear matrix inequality in addressing the invariant ellipsoid for given initial state conditions is reformulated as an objective optimization problem and tackled by iteratively optimization with relaxed linear objective. This dilated LMI scheme does not contain the multiplication of the system matrix and Lyapunov matrix variable, and thus relieves the imposed structure constraint on the Lyapunov Matrix. Also, the additional design matrix variable can help to achieve a better design performance. The design results show that the proposed approach can deliver better performances compared to the standard LMIs in terms of the achieved largest relative stability under the same control efforts and attitude constraints. The merits of this approach are demonstrated by various numerical controller constructions with different specifications regarding the certain level of relative stability and parasitic
uncertain coupling. The time-response simulations are given for
verification.