Positive invariance of linear uncertain systems and applications

Sufficient and necessary conditions for nonlinear impulsive systems with respect to linear constraints with bounded additive disturbances are obtained from a characterization of positive invariance properties for these systems. As an application of results obtained, the sufficient conditions for discrete state feedback control and for asymptotic stabilization of linear uncertain systems with the state positively nonsymmetrical invariant set are presented. Furthermore, extensions to multirate sampled-data control are presented. Finally, a numerical example is given