Practical Robust Positive Invariance for Large-Scale Discrete Time Systems

This note introduces practical set invariance notions for physically interconnected, discrete–time systems, subject to additive but bounded disturbances. We offer a concept which allows us to investigate invariance properties for each of the subsystems separately and, hence, to study invariance properties of the overall system in a sensible and decentralized way. The analysis part makes use of stability and invariance notions of properly specified set–dynamics. The developed approach provides a decentralized, non–conservative and computationally tractable way to study desirable robust positive invariance and stability notions for the corresponding set–dynamics and, in turn, for the overall system as well as to guarantee safe and independent operation of the constituting subsystems. These desirable and strong properties are inherited, under mild assumptions, from the classical stability and invariance properties of the associated vector–valued dynamics which capture in a simple but appropriate and non–conservative way the dynamical behavior induced by the underlying set–dynamics of interest. Large-scale Systems, Interconnected Systems, Set Invariance, Stability, Constraints, Uncertainty, Set–Dynamics.