Support function of minimal disturbance invariant set and its derivative: Application in designing feedback gain

This paper shows that the support function of the minimal disturbance invariant set of a linear system with additive disturbances under a linear feedback law can be evaluated with arbitrary accuracy and so does its derivative with respect to the feedback gain. These two values are applied to design a feedback gain so that the resultant minimal disturbance invariant set has optimal supports along given directions. This proposed design approach is also demonstrated by numerical examples.