The problem of construction of controlled invariant polytopic sets with specified complexity, for linear systems subject to linear state and control constraints, is investigated. First, geometric conditions for the enlargement of a polytopic set by adding a new vertex, in order to produce a polytopic set of specified complexity, are established. Next, conditions for such an enlargement of controlled invariant sets to preserve the controlled invariance property are presented. The established theoretical results are used to develop methods for the construction of admissible controlled invariant sets with specified complexity. Two numerical examples show how these results can be used for the computation of monotonic sequences of admissible controlled invariant sets of specified complexity.
Athanasopoulos, N., Bitsoris, G., & Lazar, M. (2014). Construction of invariant polytopic sets with specified complexity. International Journal of Control, 47(8), 1681-1693. https://doi.org/10.1080/00207179.2014.882518