  This paper focuses on the invariance control problem for discrete-time
switched nonlinear systems. The proposed approach computes controlled invariant
sets in a finite number of iterations and directly yields a partition-based
invariance controller using the information recorded during the computation. In
contrast with Lyapunov-based control methods, this method does not require the
subsystems to have common equilibrium points. Algorithms are developed for
computing both outer and inner approximations of the maximal controlled
invariant sets, which are represented as finite unions of intervals. The
general convergence results of interval methods allow us to obtain arbitrarily
precise approximations without any stability assumptions. In addition,
invariant inner approximations can be computed provided that the switched
system satisfies a robustly controlled invariance condition. Under the same
condition, we also prove the existence of an invariance controller based on
partitions of the state space. Our method is illustrated with three examples
drawn from different applications and compared with existing work in the
literature.
