Abstract
This paper considers linear systems which are positively invariant in a second-order cone (ice-cream cone). Three problems are addressed: (i) stability; (ii) performance; (iii) state feedback design for stabilisation and optimal performance while preserving cone invariance. We derive necessary and sufficient conditions via Linear Matrix Inequalities (LMI) for the solution of problems (i) and (ii). As for problem (iii), a full parametrization of feasible state feedback gains is provided, along with some LMI relaxations useful to compute a feasible gain. Finally, a numerical example is briefly discussed.
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