# Zonotopic ultimate bounds for linear systems with bounded disturbances

### Citation:

F. Stoican, Olaru, S., De Doná, J. A., and Seron, M. M., “Zonotopic ultimate bounds for linear systems with bounded disturbances”, in Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, p. 9224–9229.

28 August-2 Sept

### ISBN Number:

978-3-902661-93-7

### Abstract:

This paper deals with robust invariant sets construction for discrete-time linear timeinvariant dynamics. The case of a zonotopic disturbance set is analysed in detail by exploiting the properties of these geometrical structures. A constructive method is provided for diminishing the conservatism of ultimate bound invariant sets. It is shown that the resulting zonotopic set is related to the minimal robust positively invariant set in the sense that their boundaries have common points.

### DOI:

10.3182/20110828-6-IT-1002.03247