Equi-invariability, bounded invariance complexity and L-stability for control systems

TL;DR

This paper introduces new concepts of invariance and stability for control systems, providing characterizations and establishing dichotomy theorems to deepen understanding of control set behaviors.

Contribution

It defines bounded invariance complexity, mean invariance complexity, and mean L-stability, linking them to six types of equi-invariability and proving two new dichotomy theorems.

Findings

Introduced bounded invariance complexity and related notions.

Characterized these notions via six types of equi-invariability.

Established two new dichotomy theorems for control systems.

Abstract

In the paper we introduce the notions of bounded invariance complexity, bounded invariance complexity in the mean and mean L-stability for control systems. Then we characterize these notions by introducing six types of equi-invariability. As by product, two new dichotomy theorems for control system on control sets are established.