Invariance entropy for uncertain control systems

We introduce a notion of invariance entropy for uncertain control systems. This entropy extends the invariance entropy for deterministic control systems introduced by Colonius and Kawan (2009). We show that for uncertain control systems, the invariance feedback entropy, proposed by Tomar, Rungger, and Zamani (2020), is bounded from below by our invariance entropy. We generalize the formula for the calculation of entropy of invariant partitions obtained by Tomar, Kawan, and Zamani (2022) to quasi-invariant-partitions. Under some reasonable assumptions, we obtain two explicit formulas of invariance entropy for uncertain control systems and invariance feedback entropy for finite controlled invariant sets.