Characterization of Positive Invariance of Quadratic Convex Sets for Discrete-Time Systems Using Optimization Approaches

A positively invariant set is an important concept in dynamical systems. The study of conditions for discrete-time systems one interesting topic both theoretical studies and practical applications research. Different methods characterizing the invariance different types sets have been established. For example, ellipsoidal Lorenz cone, which are quadratic convex sets, properties from a polyhedral set. This paper presents optimization method dual to characterize positive cone. proposed applicable linear nonlinear Using programming induced norm, condition problems transformed into problems, also used give equivalent forms. Fewer results on cones can be found than other type set; this fulfills problem. In addition, provide more options checking perspective optimization. effectiveness demonstrated by numerical examples.