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A linear parameter varying (LPV) controller design example for the position and attitude control of a spacecraft is presented. The six degree-of freedom (DOF) model including the aerodynamics is described. Simulations with the nonlinear 6-DOF model show the usefulness of the design procedure. The practical problem of "fast dynamics" in the controller is solved by an ad hoc method based on the use of a single quadratic Lyapunov function with pole clustering constraints for each frozen linear time invariant (LTI) system in the parameter variation set. The results show that the method facilitates simulation and allows for addressing implementation aspects such as the sampling rate. Index Terms-Gain scheduling, linear matrix inequality (LMI), linear parameter varying (LPV), pole placement.

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This paper considers the problem of automatically controlling the glucose level in a Diabetes type I patient. Three issues have been considered: model uncertainty, time-varying/nonlinear phenomena and controller implementation. To that end, the dynamical model of the insulin/glucose relation is framed as a Linear Parameter Varying system and a controller is designed based on it. In addition, this framework allows not only a better performance than other classical methods, but also provides stability and performance guarantees. Design computations are based on convex Linear Matrix Inequality (LMI) optimization. Implementation is based on a low order controller whose dynamics adapts according to the glucose levels measured in real-time.

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