Robust state feedback stabilisation of positive LTI systems with polytopic uncertainty

This paper deals with the robust state feedback stabilizability problem of linear time-invariant (LTI) systems in the presenceof polytopic uncertainty. The paper contributes two major results involving (i) necessary and sufficient conditions to simultaneouslycheck positivity and robust stability of an uncertain LTI system (ii) the development of a design algorithm to solve the mainstabilizability problem. This problem is not easy to deal with because it is not a convex problem. To cope with this issue, a designalgorithm is proposed that checks the design space of the stabilizer parameters, divides it into smaller subspaces, checks thefeasibility of the corner points of the design subspaces, removes the detected total infeasible design subspaces, and shrinks theremaining parts to solve the design problem, iteratively. The proposed algorithm is applied to the cancer chemotherapy applicationand the results demonstrate its efficacy to control the model considering the positivity condition.