Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints

Abstract We consider the problem of computing maximal invariant set discrete-time linear systems subject to a class non-convex constraints that admit quadratic relaxations. These include semialgebraic sets and other smooth with Lipschitz gradient. With these relaxations, sufficient condition for invariance is derived it can be formulated as matrix inequalities. Based on condition, new algorithm presented finite-time convergence actual under mild assumptions. This also extended switched some special nonlinear systems. The performance this demonstrated several numerical examples.