Positively invariant sets of discrete-time systems with constrained inputs

Linear discrete-time dynamical systems x k+1 =Ax k +c k with constrained inputs c k ∈Ω, for which the matrix A possesses the property of leaving a proper cone K + positively invariant, i.e. AK + ⊂K + . Necessary and sufficient conditions guarantee that a non-empty set D(K; a, b)⊂R n , obtained from the intersection of translated proper cones, is positively invariant for motions of the system. Both the homogeneous and inhomogeous cases are considered. It is shown how the results presented can be used to solve the saturated state feedback regulator problem

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