A One-step Approach to Computing a Polytopic Robust Positively Invariant Set
For control engineers, this provides a computationally efficient alternative to iterative methods for computing RPI sets.
The paper presents a one-step LP-based method to compute a minimal robust positively invariant set for linear discrete-time systems with bounded disturbances, achieving minimality within a predefined polytope family.
A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the solving of a single LP, a polytopic RPI set that is minimal with respect to the family of RPI sets generated from a finite number of inequalities with pre-defined normal vectors.