Influence of complexity relaxation and convex hull manipulation on LMI based control design

The paper investigates how the complexity and the convex hull determined by the vertexes of the TP model representation of a given quasi Linear Parameter Varying state-space model influence the stable parameter region achievable via Linear Matrix Inequality based control design. The paper applies the Relaxed TP model transformation based Control Design Framework that supports both the complexity-accuracy trade-off of the TP model representation and convex hull manipulation separately executable on all components of the control system to be derived. Some specialization and further relaxation of the framework is also proposed here for frequent cases when all components of the system is handled in TP model form. The framework is also extended with a TP model interpolation technique to perform a systematic convex hull manipulation. The overall investigation is done on the complex NATA model of the three degree of freedom aeroelastic wing section model including Stribeck friction. The paper concludes and via the example proofs that both the complexity and the convex hull strongly influences the feasibility of the design. Further the paper proofs that the separate convex hull manipulation of the given model done for controller and the observer design also has to be taken into consideration.